TEST_VALUES
Sample Function Values

TEST_VALUES is a MATLAB library which returns a few selected values of various functions.

The intent of TEST_VALUES is to provide a means of making very simple tests for correctness of software designed to compute a variety of functions. The testing can be done automatically. The data provided is generally skimpy, and might not test the algorithm over a suitably wide range. It does, however, provide a small amount of reassurance that a given computation is (or is not) computing the appropriate quantity, and doing so reasonably accurately.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

TEST_VALUES is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATHEMATICA version and a MATLAB version.

Related Data and Programs:

CORDIC, a MATLAB library which use the CORDIC method to compute certain elementary functions.

FN, a MATLAB library which approximates elementary and special functions using Chebyshev polynomials, by Wayne Fullerton.

GSL, a C++ library which evaluates many special functions.

LEGENDRE_POLYNOMIAL, a MATLAB library which evaluates the Legendre polynomial and associated functions.

POLPAK, a MATLAB library which computes various mathematical functions; test values for many of these functions are available in TEST_VALUES.

PROB, a MATLAB library which computes various statistical functions; test values for many of these functions are available in TEST_VALUES.

SPECFUN, a FORTRAN77 library which computes various special functions, particularly Bessel functions.

STEAM, a FORTRAN90 library which computes various functions related to the physical properties of water; test values for many of these functions are available in TEST_VALUES.

Reference:

1. Milton Abramowitz, Irene Stegun,
   Handbook of Mathematical Functions,
   National Bureau of Standards, 1964,
   ISBN: 0-486-61272-4,
   LC: QA47.A34.
2. Robert Corless, Gaston Gonnet, David Hare, David Jeffrey, Donald Knuth,
   On the Lambert W Function,
   Advances in Computational Mathematics,
   Volume 5, 1996, pages 329-359.
3. Gerard Cornuejols, Regina Urbaniak, Robert Weismantel, Laurence Wolsey,
   Decomposition of Integer Programs and of Generating Sets,
   in Algorithms - ESA '97,
   Lecture Notes in Computer Science 1284,
   edited by R Burkard, G Woeginger,
   Springer, 1997, pages 92-103,
   LC: QA76.9.A43.E83.
4. Marc Deleglise, Joel Rivat,
   Computing the Summation of the Moebius Function,
   Experimental Mathematics,
   Volume 5, 1996, pages 291-295.
5. Lester Haar, John Gallagher, George Kell,
   NBS/NRC Steam Tables:
   Thermodynamic and Transport Properties and Computer Programs for Vapor and Liquid States of Water in SI Units,
   Hemisphere Publishing Corporation, Washington, 1984,
   ISBN: 0-89116-353-0,
   LC: TJ270.H3.
6. Brian Hayes,
   "Why W?",
   The American Scientist,
   Volume 93, March-April 2005, pages 104-108.
7. Kanti Mardia, Peter Jupp,
   Directional Statistics,
   Wiley, 2000,
   ISBN: 0471953334,
   LC: QA276.M335
8. Allan McLeod,
   Algorithm 757: MISCFUN: A software package to compute uncommon special functions,
   ACM Transactions on Mathematical Software,
   Volume 22, Number 3, September 1996, pages 288-301.
9. National Bureau of Standards,
   Tables of the Bivariate Normal Distribution and Related Functions,
   Applied Mathematics Series, Number 50, 1959.
10. Robert Owens,
    An Algorithm to Solve the Frobenius Problem,
    Mathematics Magazine,
    Volume 76, Number 4, October 2003, 264-275.
11. Karl Pearson,
    Tables of the Incomplete Beta Function,
    Cambridge University Press, 1968,
    ISBN: 0521059224,
    LC: QA351.P38.
12. Frank Powell,
    Statistical Tables for Sociology, Biology and Physical Sciences,
    Cambridge University Press, 1982,
    ISBN: 0521284732,
    LC: QA276.25.S73.
13. Edward Reingold, Nachum Dershowitz,
    Calendrical Calculations: The Millennium Edition,
    Cambridge University Press, 2001,
    ISBN: 0-521-77752-6,
    LC: CE12.R45.
14. Johannes van der Corput,
    Verteilungsfunktionen,
    Proc Akad Amsterdam,
    Volume 38, 1935,
    Volume 39, 1936.
15. Eric Weisstein,
    CRC Concise Encyclopedia of Mathematics,
    CRC Press, 2002,
    Second edition,
    ISBN: 1584883472,
    LC: QA5.W45
16. Stephen Wolfram,
    The Mathematica Book,
    Fourth Edition,
    Cambridge University Press, 1999,
    ISBN: 0-521-64314-7,
    LC: QA76.95.W65.
17. Shanjie Zhang, Jianming Jin,
    Computation of Special Functions,
    Wiley, 1996,
    ISBN: 0-471-11963-6,
    LC: QA351.C45.
18. Daniel Zwillinger, editor,
    CRC Standard Mathematical Tables and Formulae,
    30th Edition,
    CRC Press, 1996,
    ISBN: 0-8493-2479-3,
    LC: QA47.M315.
19. Daniel Zwillinger, Steven Kokoska,
    Standard Probability and Statistical Tables,
    CRC Press, 2000,
    ISBN: 1-58488-059-7,
    LC: QA273.3.Z95.

Source Code:

• abram0_values.m, returns selected values of the Abramowitz function of order 0.
• abram1_values.m, returns selected values of the Abramowitz function of order 1.
• abram2_values.m, returns selected values of the Abramowitz function of order 2.
• agm_values.m, returns selected values of the arithmetic geometric mean function.
• airy_ai_values.m, returns selected values of the Airy Ai function.
• airy_ai_int_values.m, returns selected values of the integral of the Airy Ai function.
• airy_ai_prime_values.m, returns selected values of the derivative of the Airy function Ai.
• airy_bi_values.m, returns selected values of the Airy Bi function.
• airy_bi_int_values.m, returns selected values of the integral of the Airy Bi function.
• airy_bi_prime_values.m, returns selected values of the derivative of the Airy function Bi.
• airy_cai_values.m, returns selected values of the Airy Ai function for complex argument.
• airy_cbi_values.m, returns selected values of the Airy Bi function for complex argument.
• airy_gi_values.m, returns selected values of the Airy Gi function.
• airy_hi_values.m, returns selected values of the Airy Hi function.
• arccos_values.m, returns selected values of the arc cosine function.
• arccosh_values.m, returns selected values of the hyperbolic arc cosine function.
• arcsin_values.m, returns selected values of the arc sine function.
• arcsinh_values.m, returns selected values of the hyperbolic arc sine function.
• arctan_values.m, returns selected values of the arc tangent function.
• arctan_int_values.m, returns selected values of the arctangent integral.
• arctan2_values.m, returns selected values of the arc tangent function of two arguments.
• arctanh_values.m, returns selected values of the hyperbolic arc tangent function.
• bei0_values.m, returns selected values of the Kelvin BEI function for NU = 0.
• bei1_values.m, returns selected values of the Kelvin BEI function for NU = 1.
• bell_values.m, returns selected values of the Bell numbers.
• ber0_values.m, returns selected values of the Kelvin BER function for NU = 0.
• ber1_values.m, returns selected values of the Kelvin BER function for NU = 1.
• bernoulli_number_values.m, returns selected values of the Bernoulli numbers.
• bernoulli_poly_values.m, returns selected values of the Bernoulli polynomials.
• bernstein_poly_values.m, returns selected values of the Bernstein polynomials.
• bessel_i0_int_values.m returns some values of the integral of the I0 Bessel function.
• bessel_i0_spherical_values.m returns some values of the spherical Bessel function i0.
• bessel_i0_values.m returns some values of the I0 Bessel function.
• bessel_i1_spherical_values.m returns some values of the spherical Bessel function i1.
• bessel_i1_values.m returns some values of the I1 Bessel function.
• bessel_in_values.m returns some values of the In Bessel function.
• bessel_ix_values.m returns some values of the In Bessel function for NONINTEGER order.
• bessel_j0_int_values.m returns some values of the integral of the J0 Bessel function.
• bessel_j0_spherical_values.m returns some values of the Spherical Bessel function j0.
• bessel_j0_values.m returns some values of the J0 Bessel function.
• bessel_j1_spherical_values.m returns some values of the Spherical Bessel function j1.
• bessel_j1_values.m returns some values of the J1 Bessel function.
• bessel_jn_values.m returns some values of the Jn Bessel function.
• bessel_jx_values.m returns some values of the Jn Bessel function for NONINTEGER order.
• bessel_k0_int_values.m returns some values of the integral of the K0 Bessel function.
• bessel_k0_values.m returns some values of the K0 Bessel function.
• bessel_k1_values.m returns some values of the K1 Bessel function.
• bessel_kn_values.m returns some values of the Kn Bessel function.
• bessel_kx_values.m returns some values of the Kn Bessel function for NONINTEGER order.
• bessel_y0_int_values.m returns some values of the integral of the Y0 Bessel function.
• bessel_y0_spherical_values.m returns some values of the Spherical Bessel function y0.
• bessel_y0_values.m returns some values of the Y0 Bessel function.
• bessel_y1_spherical_values.m returns some values of the Spherical Bessel function y1.
• bessel_y1_values.m returns some values of the Y1 Bessel function.
• bessel_yn_values.m returns some values of the Yn Bessel function.
• bessel_yx_values.m returns some values of the Yn Bessel function for NONINTEGER order.
• beta_cdf_values.m returns some values of the Beta CDF.
• beta_inc_values.m returns some values of the incomplete Beta function.
• beta_log_values.m returns some values of the logarithm of the Beta function.
• beta_noncentral_cdf_values.m returns some values of the noncentral incomplete Beta function.
• beta_values.m returns some values of the Beta function.
• binomial_values.m returns some values of the binomial coefficients.
• binomial_cdf_values.m returns some values of the binomial CDF.
• bivariate_normal_cdf_values.m returns some values of the bivariate normal CDF.
• catalan_values.m returns some values of the Catalan numbers.
• cauchy_cdf_values.m returns some values of the Cauchy CDF.
• cbrt_values.m returns some values of the cube root function.
• cheby_t_poly_values.m returns values of the Chebyshev polynomial T(n,x).
• cheby_u_poly_values.m returns values of the Chebyshev polynomial U(n,x).
• cheby_v_poly_values.m returns values of the Chebyshev polynomial V(n,x).
• cheby_w_poly_values.m returns values of the Chebyshev polynomial W(n,x).
• chi_values.m returns some values of the hyperbolic cosine integral function.
• chi_square_cdf_values.m returns some values of the Chi-Square CDF.
• chi_square_noncentral_cdf_values.m returns some values of the noncentral Chi-Square CDF.
• ci_values.m returns some values of the cosine integral function.
• cin_values.m returns some values of the alternate cosine integral function.
• cinh_values.m returns some values of the alternate hyperbolic cosine integral function.
• clausen_values.m returns some values of Clausen's integral function.
• clebsch_gordan_values.m returns some values of the Clebsch-Gordan coefficients.
• collatz_count_values.m returns some values of the length of the Collatz sequence.
• cos_values.m returns some values of the cosine function.
• cos_degree_values.m returns some values of the cosine function for arguments in degrees.
• cos_power_int_values.m returns some values of the integral of the N-th power of the cosine function;
• cosh_values.m returns some values of the hyperbolic cosine function.
• cot_values.m returns some values of the cotangent function.
• cp_values.m returns some values of the specific heat at constant pressure.
• dawson_values.m returns some values of Dawson's integral.
• debye1_values.m returns some values of the Debye1 function of order 1.
• debye2_values.m returns some values of the Debye1 function of order 2.
• debye3_values.m returns some values of the Debye1 function of order 3.
• debye4_values.m returns some values of the Debye1 function of order 4.
• dedekind_sum_values.m returns some values of the Dedekind sum.
• dielectric_values.m returns some values of the static dielectric constant.
• dilogarithm_values.m returns some values of the dilogarithm function.
• e1_values.m returns some values of the exponential integral function E1(X).
• ei_values.m returns some values of the exponential integral function EI(X).
• elliptic_ea_values.m returns values of the complete elliptic integral E(ALPHA).
• elliptic_em_values.m returns values of the complete elliptic integral E(M).
• elliptic_ka_values.m returns values of the complete elliptic integral K(ALPHA).
• elliptic_km_values.m returns values of the complete elliptic integral K(M).
• erf_values.m returns some values of the ERF or "error" function.
• erfc_values.m returns some values of the ERFC or "complementary error" function.
• euler_number_values.m returns some values of the Euler numbers.
• euler_poly_values.m returns some values of the Euler polynomials.
• exp_values.m returns some values of the exponential function.
• exp3_int_values.m returns some values of the EXP3 integral function.
• exponential_cdf_values.m returns some values of the exponential CDF.
• extreme_values_cdf_values.m returns some values of the extreme_values CDF.
• f_cdf_values.m returns some values of the F CDF.
• f_noncentral_cdf_values.m returns some values of the noncentral F CDF.
• factorial_values.m returns values of the factorial function.
• factorial2_values.m returns values of the double factorial function.
• factorial_rising_values.m returns values of the integer Pochhammer function.
• fresnel_cos_values.m returns some values of the Fresnel cosine integral function.
• fresnel_sin_values.m returns some values of the Fresnel sine integral function.
• frobenius_number_order2_values.m returns some values of the Frobenius number of order2.
• frobenius_number_order_values.m returns some order values for the general Frobenius number problem.
• frobenius_number_data_values.m returns some data values for the general Frobenius number problem.
• gamma_cdf_values.m, returns selected values of the Gamma CDF.
• gamma_inc_p_values.m, returns selected values of the incomplete Gamma P function.
• gamma_inc_q_values.m, returns selected values of the incomplete Gamma Q function.
• gamma_inc_tricomi_values.m, returns selected values of Tricomi's incomplete Gamma function.
• gamma_inc_values.m, returns selected values of the incomplete Gamma function.
• gamma_log_values.m returns some values of the logarithm of the Gamma function.
• gamma_values.m, returns selected values of the Gamma function.
• gegenbauer_poly_values.m returns some values of the Gegenbauer polynomials.
• geometric_cdf_values.m returns some values of the geometric CDF.
• goodwin_values.m returns some values of the Goodwin function.
• gud_values.m returns some values of the Gudermannian function.
• hermite_function_values.m returns some values of the Hermite function Hf(n,x).
• hermite_poly_phys_values.m returns some values of the physicist's Hermite polynomial H(n,x).
• hermite_poly_prob_values.m returns some values of the probabilist's Hermite polynomial He(n,x).
• hyper_1f1_values.m returns some values of the hypergeometric 1F1 function.
• hyper_2f1_values.m returns some values of the hypergeometric 2F1 function.
• hypergeometric_cdf_values.m returns some values of the hypergeometric CDF.
• hypergeometric_pdf_values.m returns some values of the hypergeometric PDF.
• hypergeometric_u_values.m returns some values of the hypergeometric function U(a,b,x).
• i0ml0_values.m returns some values of the I0ML0 function.
• i1ml1_values.m returns some values of the I1ML1 function.
• int_values.m returns some values of the "int" function.
• jacobi_cn_values.m returns some values of the Jacobi elliptic function CN(A,X).
• jacobi_dn_values.m returns some values of the Jacobi elliptic function dN(A,X).
• jacobi_poly_values.m returns some values of the Jacobi polynomial.
• jacobi_sn_values.m returns some values of the Jacobi elliptic function SN(A,X).
• jed_ce_values.m returns some values of the Julian Ephemeris Date and the corresponding Common Era year/month/day/fraction date.
• jed_mjd_values.m returns some values of the Julian Ephemeris Date and the corresponding Modified Julian Day count.
• jed_rd_values.m returns some values of the Julian Ephemeris Date and the corresponding Reingold Dershowitz date.
• jed_weekday_values.m returns some values of the Julian Ephemeris Date and the day of the week.
• kei0_values.m, returns selected values of the Kelvin KEI function for NU = 0.
• kei1_values.m, returns selected values of the Kelvin KEI function for NU = 1.
• ker0_values.m, returns selected values of the Kelvin KER function for NU = 0.
• ker1_values.m, returns selected values of the Kelvin KER function for NU = 1.
• laguerre_associated_values.m returns values of associated Laguerre functions.
• laguerre_general_values.m returns values of generalized Laguerre functions.
• laguerre_polynomial_values.m returns some values of the Laguerre polynomial.
• lambert_w_values.m returns values of the Lambert W function.
• laplace_cdf_values.m returns values of the Laplace CDF.
• legendre_associated_values.m returns values of associated Legendre functions.
• legendre_associated_normalized_values.m returns values of the normalized associated Legendre functions.
• legendre_function_q_values.m returns values of the Legendre Q function.
• legendre_poly_values.m returns values of the Legendre polynomials.
• lerch_values.m returns values of the Lerch transcendent function.
• linear_system_values.m returns some linear systems.
• lobachevsky_values.m returns values of the Lobachevsky function.
• log_values.m returns some values of the natural logarithm function.
• log_normal_cdf_values.m returns values of the LogNormal CDF.
• log_series_cdf_values.m returns values of the LogSeries CDF.
• log10_values.m returns some values of the logarithm base 10 function.
• logarithmic_integral_values.m returns values of the logarithmic integral.
• logistic_cdf_values.m returns values of the logistic CDF.
• mertens_values.m returns some values of the Mertens function.
• moebius_values.m returns some values of the Moebius function.
• negative_binomial_cdf_values.m returns some values of the Negative Binomial CDF.
• nine_j_values.m returns some values of the Wigner 9J coefficients;
• normal_cdf_values.m returns some values of the Normal CDF.
• normal_01_cdf_values.m returns values of the Normal01 CDF.
• omega_values.m returns some values of the OMEGA function.
• owen_values.m returns some values of Owen's T function.
• partition_count_values.m returns some values of the integer partition count.
• partition_distinct_count_values.m returns some values of Q(N).
• phi_values.m returns some values of the PHI function.
• pi_values.m returns some values of the PI function.
• pochhammer_values.m returns some values of the Pochhammer function.
• poisson_cdf_values.m returns some values of the Poisson CDF.
• polylogarithm_values.m returns some values of the polylogarithm function.
• prandtl_values.m returns some values of the Prandtl number.
• prime_values.m returns some values of the prime function.
• psat_values.m returns some values of the saturation pressure.
• psi_values.m returns some values of the Psi or Digamma function.
• r8_factorial_values.m returns values of the real factorial function.
• r8_factorial_log_values.m returns values of log(n!).
• rayleigh_values.m returns some values of the Rayleigh CDF.
• secvir_values.m returns some values of the second virial coefficient.
• shi_values.m returns some values of the hyperbolic sine integral function.
• si_values.m returns some values of the sine integral function.
• sigma_values.m returns some values of the Sigma function.
• sin_values.m returns some values of the sine function.
• sin_degree_values.m returns some values of the sine function for arguments in degrees.
• sin_power_int_values.m returns some values of the integral of the N-th power of the sine function;
• sinh_values.m returns some values of the hyperbolic sine function.
• six_j_values.m returns some values of the Wigner 6J coefficients;
• sound_values_values.m returns some values of the speed of sound.
• sphere_unit_area_values.m returns some values of the area of the unit sphere in various dimensions.
• sphere_unit_volume_values.m returns some values of the volume of the unit sphere in various dimensions.
• spherical_harmonic_values.m returns some values of the spherical harmonic function.
• sqrt_values.m returns some values of the square root function.
• stirling1_values.m returns some values of the Stirling numbers of the first kind.
• stirling2_values.m returns some values of the Stirling numbers of the second kind.
• stromgen_values.m returns some values of the Stromgen integral function.
• struve_h0_values.m returns some values of the Struve H0 function.
• struve_h1_values.m returns some values of the Struve H1 function.
• struve_l0_values.m returns some values of the Struve L0 function.
• struve_l1_values.m returns some values of the Struve L1 function.
• student_cdf_values.m returns some values of the Student CDF.
• student_noncentral_cdf_values.m returns some values of the noncentral Student CDF.
• subfactorial_values.m returns values of the subfactorial function.
• surten_values.m returns some values of the surface tension.
• synch1_values.m returns some values of the synchrotron function 1.
• synch2_values.m returns some values of the synchrotron function 2.
• tan_values.m returns some values of the tangent function.
• tanh_values.m returns some values of the hyperbolic tangent function.
• tau_values.m returns some values of the Tau function.
• thercon_values.m returns some values of the thermal conductivity.
• three_j_values.m returns some values of the Wigner 3J coefficients;
• timestamp.m, prints the YMDHMS date as a timestamp.
• tran02_values.m returns some values of the transportation function of order 2.
• tran03_values.m returns some values of the transportation function of order 3.
• tran04_values.m returns some values of the transportation function of order 4.
• tran05_values.m returns some values of the transportation function of order 5.
• tran06_values.m returns some values of the transportation function of order 6.
• tran07_values.m returns some values of the transportation function of order 7.
• tran08_values.m returns some values of the transportation function of order 8.
• tran09_values.m returns some values of the transportation function of order 9.
• trigamma_values.m returns some values of the TriGamma function.
• tsat_values.m returns some values of the saturation temperature.
• van_der_corput_values.m returns some values of the van der Corput sequence.
• viscosity_values.m returns some values of the viscosity function.
• von_mises_cdf_values.m returns some values of the von Mises CDF.
• weekday_values.m returns some values of the day of the week for given Y/M/D dates in the Common Era Julian/Gregorian calendar.
• weibull_cdf_values.m returns some values of the Weibull CDF.
• zeta_values.m returns some values of the Riemann Zeta function.

Examples and Tests:

• test_values_test.m, runs all the tests.
• test_values_test_output.txt, the output from a run of the sample program.
• test_values_test001.m, tests ABRAM0_VALUES.
• test_values_test002.m, tests ABRAM1_VALUES.
• test_values_test003.m, tests ABRAM2_VALUES.
• test_values_test0035.m, tests AGM_VALUES.
• test_values_test004.m, tests AIRY_AI_VALUES.
• test_values_test005.m, tests AIRY_AI_INT_VALUES.
• test_values_test006.m, tests AIRY_AI_PRIME_VALUES.
• test_values_test007.m, tests AIRY_BI_VALUES.
• test_values_test008.m, tests AIRY_BI_INT_VALUES.
• test_values_test009.m, tests AIRY_BI_PRIME_VALUES.
• test_values_test0093.m, tests AIRY_CAI_VALUES.
• test_values_test0095.m, tests AIRY_CBI_VALUES.
• test_values_test010.m, tests AIRY_GI_VALUES.
• test_values_test011.m, tests AIRY_HI_VALUES.
• test_values_test0114.m, tests ARCCOS_VALUES.
• test_values_test01145.m, tests ARCCOSH_VALUES.
• test_values_test0115.m, tests ARCSIN_VALUES.
• test_values_test01155.m, tests ARCSINH_VALUES.
• test_values_test0116.m, tests ARCTAN_VALUES.
• test_values_test012.m, tests ARCTAN_INT_VALUES.
• test_values_test0123.m, tests ARCTANH_VALUES.
• test_values_test0127.m, tests BEI0_VALUES.
• test_values_test0128.m, tests BEI1_VALUES.
• test_values_test013.m, tests BELL_VALUES.
• test_values_test0134.m, tests BER0_VALUES.
• test_values_test0135.m, tests BER1_VALUES.
• test_values_test014.m, tests BERNOULLI_NUMBER_VALUES.
• test_values_test015.m, tests BERNOULLI_POLY_VALUES.
• test_values_test016.m, tests BERNSTEIN_POLY_VALUES.
• test_values_test017.m, tests BESSEL_I0_VALUES.
• test_values_test018.m, tests BESSEL_I0_INT_VALUES.
• test_values_test0185.m, tests BESSEL_I0_SPHERICAL_VALUES.
• test_values_test019.m, tests BESSEL_I1_VALUES.
• test_values_test0195.m, tests BESSEL_I1_SPHERICAL_VALUES.
• test_values_test020.m, tests BESSEL_IN_VALUES.
• test_values_test0205.m, tests BESSEL_IX_VALUES.
• test_values_test021.m, tests BESSEL_J0_VALUES.
• test_values_test022.m, tests BESSEL_J0_INT_VALUES.
• test_values_test023.m, tests BESSEL_J0_SPHERICAL_VALUES.
• test_values_test024.m, tests BESSEL_J1_VALUES.
• test_values_test025.m, tests BESSEL_J1_SPHERICAL_VALUES.
• test_values_test026.m, tests BESSEL_JN_VALUES.
• test_values_test0265.m, tests BESSEL_JX_VALUES.
• test_values_test027.m, tests BESSEL_K0_VALUES.
• test_values_test028.m, tests BESSEL_K0_INT_VALUES.
• test_values_test029.m, tests BESSEL_K1_VALUES.
• test_values_test030.m, tests BESSEL_KN_VALUES.
• test_values_test0305.m, tests BESSEL_KX_VALUES.
• test_values_test031.m, tests BESSEL_Y0_VALUES.
• test_values_test032.m, tests BESSEL_Y0_INT_VALUES.
• test_values_test033.m, tests BESSEL_Y0_SPHERICAL_VALUES.
• test_values_test034.m, tests BESSEL_Y1_VALUES.
• test_values_test035.m, tests BESSEL_Y1_SPHERICAL_VALUES.
• test_values_test036.m, tests BESSEL_YN_VALUES.
• test_values_test0365.m, tests BESSEL_YX_VALUES.
• test_values_test037.m, tests BETA_CDF_VALUES.
• test_values_test038.m, tests BETA_INC_VALUES.
• test_values_test039.m, tests BETA_LOG_VALUES.
• test_values_test0395.m, tests BETA_NONCENTRAL_CDF_VALUES.
• test_values_test040.m, tests BETA_VALUES.
• test_values_test041.m, tests BINOMIAL_VALUES.
• test_values_test042.m, tests BINOMIAL_CDF_VALUES.
• test_values_test0425.m, tests BIVARIATE_NORMAL_CDF_VALUES.
• test_values_test043.m, tests CATALAN_VALUES.
• test_values_test044.m, tests CAUCHY_CDF_VALUES.
• test_values_test0445.m, tests CBRT_VALUES.
• test_values_test045.m, tests CHEBY_T_POLY_VALUES.
• test_values_test046.m, tests CHEBY_U_POLY_VALUES.
• test_values_test0465.m, tests CHI_VALUES.
• test_values_test047.m, tests CHI_SQUARE_CDF_VALUES.
• test_values_test048.m, tests CHI_SQUARE_NONCENTRAL_CDF_VALUES.
• test_values_test049.m, tests CI_VALUES.
• test_values_test050.m, tests CIN_VALUES.
• test_values_test051.m, tests CLAUSEN_VALUES.
• test_values_test05125.m, tests CLEBSCH_GORDAN_VALUES.
• test_values_test0515.m, tests COLLATZ_COUNT_VALUES.
• test_values_test0517.m, tests COS_VALUES.
• test_values_test0519.m, tests COSH_VALUES.
• test_values_test052.m, tests CP_VALUES.
• test_values_test053.m, tests DAWSON_VALUES.
• test_values_test054.m, tests DEBYE1_VALUES.
• test_values_test055.m, tests DEBYE2_VALUES.
• test_values_test056.m, tests DEBYE3_VALUES.
• test_values_test057.m, tests DEBYE4_VALUES.
• test_values_test0575.m, tests DEDEKIND_SUM_VALUES.
• test_values_test058.m, tests DIELECTRIC_VALUES.
• test_values_test059.m, tests DILOGARITHM_VALUES.
• test_values_test060.m, tests E1_VALUES.
• test_values_test061.m, tests EI_VALUES.
• test_values_test062.m, tests ELLIPTIC_EA_VALUES.
• test_values_test063.m, tests ELLIPTIC_EM_VALUES.
• test_values_test064.m, tests ELLIPTIC_KA_VALUES.
• test_values_test065.m, tests ELLIPTIC_KM_VALUES.
• test_values_test066.m, tests ERF_VALUES.
• test_values_test0665.m, tests ERFC_VALUES.
• test_values_test067.m, tests EULER_NUMBER_VALUES.
• test_values_test068.m, tests EULER_POLY_VALUES.
• test_values_test0685.m, tests EXP_VALUES.
• test_values_test069.m, tests EXP3_INT_VALUES.
• test_values_test070.m, tests EXPONENTIAL_CDF_VALUES.
• test_values_test071.m, tests EXTREME_VALUES_CDF_VALUES.
• test_values_test072.m, tests F_CDF_VALUES.
• test_values_test073.m, tests F_NONCENTRAL_CDF_VALUES.
• test_values_test074.m, tests FRESNEL_COS_VALUES.
• test_values_test075.m, tests FRESNEL_SIN_VALUES.
• test_values_test0756.m, tests FROBENIUS_NUMBER_ORDER_VALUES and FROBENIUS_NUMBER_DATA_VALUES.
• test_values_test0755.m, tests FROBENIUS_NUMBER_ORDER2_VALUES.
• test_values_test076.m, tests GAMMA_VALUES.
• test_values_test077.m, tests GAMMA_CDF_VALUES.
• test_values_test078.m, tests GAMMA_INC_VALUES.
• test_values_test079.m, tests GAMMA_LOG_VALUES.
• test_values_test080.m, tests GEGENBAUER_POLY_VALUES.
• test_values_test081.m, tests GEOMETRIC_CDF_VALUES.
• test_values_test082.m, tests GOODWIN_VALUES.
• test_values_test083.m, tests GUD_VALUES.
• test_values_test0835.m, tests HERMITE_FUNCTION_VALUES.
• test_values_test084.m, tests HERMITE_POLY_PHYS_VALUES.
• test_values_test0843.m, tests HERMITE_POLY_PROB_VALUES.
• test_values_test0845.m, tests HYPER_2F1_VALUES.
• test_values_test085.m, tests HYPERGEOMETRIC_CDF_VALUES.
• test_values_test0855.m, tests HYPERGEOMETRIC_PDF_VALUES.
• test_values_test086.m, tests FACTORIAL_VALUES.
• test_values_test087.m, tests FACTORIAL2_VALUES.
• test_values_test088.m, tests POCHHAMMER_VALUES.
• test_values_test089.m, tests I0ML0_VALUES.
• test_values_test090.m, tests I1ML1_VALUES.
• test_values_test091.m, tests JACOBI_CN_VALUES.
• test_values_test092.m, tests JACOBI_DN_VALUES.
• test_values_test093.m, tests JACOBI_POLY_VALUES.
• test_values_test094.m, tests JACOBI_SN_VALUES.
• test_values_test0945.m, tests JED_CE_VALUES.
• test_values_test095.m, tests JED_MJD_VALUES.
• test_values_test096.m, tests JED_RD_VALUES.
• test_values_test097.m, tests JED_WEEKDAY_VALUES.
• test_values_test0972.m, tests KEI0_VALUES.
• test_values_test0973.m, tests KEI1_VALUES.
• test_values_test0974.m, tests KER0_VALUES.
• test_values_test0975.m, tests KER1_VALUES.
• test_values_test098.m, tests LAGUERRE_ASSOCIATED_VALUES.
• test_values_test099.m, tests LAGUERRE_POLYNOMIAL_VALUES.
• test_values_test0995.m, tests LAMBERT_W_VALUES.
• test_values_test100.m, tests LAPLACE_CDF_VALUES.
• test_values_test101.m, tests LEGENDRE_ASSOCIATED_VALUES.
• test_values_test1015.m, tests LEGENDRE_ASSOCIATED_NORMALIZED_VALUES.
• test_values_test1016.m, tests LEGENDRE_ASSOCIATED_NORMALIZED_SPHERE_VALUES.
• test_values_test102.m, tests LEGENDRE_POLY_VALUES.
• test_values_test103.m, tests LEGENDRE_FUNCTION_Q_VALUES.
• test_values_test1035.m, tests LERCH_VALUES.
• test_values_test1037.m, tests LOG_VALUES.
• test_values_test104.m, tests LOBACHEVSKY_VALUES.
• test_values_test105.m, tests LOG_NORMAL_CDF_VALUES.
• test_values_test106.m, tests LOG_SERIES_CDF_VALUES.
• test_values_test107.m, tests LOGARITHMIC_INTEGRAL_VALUES.
• test_values_test108.m, tests LOGISTIC_CDF_VALUES.
• test_values_test10875.m, tests MERTENS_VALUES.
• test_values_test109.m, tests MOEBIUS_VALUES.
• test_values_test110.m, tests NEGATIVE_BINOMIAL_CDF_VALUES.
• test_values_test1105.m, tests NINE_J_VALUES.
• test_values_test111.m, tests NORMAL_CDF_VALUES.
• test_values_test112.m, tests NORMAL_01_CDF_VALUES.
• test_values_test113.m, tests OMEGA_VALUES.
• test_values_test1135.m, tests OWEN_VALUES.
• test_values_test114.m, tests PARTITION_COUNT_VALUES.
• test_values_test115.m, tests PARTITION_DISTINCT_COUNT_VALUES.
• test_values_test116.m, tests PHI_VALUES.
• test_values_test117.m, tests PI_VALUES.
• test_values_test118.m, tests POISSON_CDF_VALUES.
• test_values_test1185.m, tests POLYLOGARITHM_VALUES.
• test_values_test119.m, tests PRANDTL_VALUES.
• test_values_test120.m, tests PRIME_VALUES.
• test_values_test121.m, tests PSAT_VALUES.
• test_values_test122.m, tests PSI_VALUES.
• test_values_test123.m, tests R8_FACTORIAL_VALUES.
• test_values_test124.m, tests R8_FACTORIAL_LOG_VALUES.
• test_values_test125.m, tests SECVIR_VALUES.
• test_values_test1255.m, tests SHI_VALUES.
• test_values_test126.m, tests SI_VALUES.
• test_values_test127.m, tests SIGMA_VALUES.
• test_values_test1275.m, tests SIN_VALUES.
• test_values_test128.m, tests SIN_POWER_INT_VALUES.
• test_values_test1283.m, tests SINH_VALUES.
• test_values_test1285.m, tests SIX_J_VALUES.
• test_values_test129.m, tests SOUND_VALUES.
• test_values_test131.m, tests SPHERE_UNIT_AREA_VALUES.
• test_values_test132.m, tests SPHERE_UNIT_VOLUME_VALUES.
• test_values_test1325.m, tests SPHERICAL_HARMONIC_VALUES.
• test_values_test130.m, tests SQRT_VALUES.
• test_values_test133.m, tests STIRLING1_VALUES.
• test_values_test134.m, tests STIRLING2_VALUES.
• test_values_test135.m, tests STROMGEN_VALUES.
• test_values_test136.m, tests STRUVE_H0_VALUES.
• test_values_test137.m, tests STRUVE_H1_VALUES.
• test_values_test138.m, tests STRUVE_L0_VALUES.
• test_values_test139.m, tests STRUVE_L1_VALUES.
• test_values_test140.m, tests STUDENT_CDF_VALUES.
• test_values_test141.m, tests STUDENT_NONCENTRAL_CDF_VALUES.
• test_values_test1415.m, tests SUBFACTORIAL_VALUES.
• test_values_test142.m, tests SURTEN_VALUES.
• test_values_test143.m, tests SYNCH1_VALUES.
• test_values_test144.m, tests SYNCH2_VALUES.
• test_values_test1445.m, tests TAN_VALUES.
• test_values_test1447.m, tests TANH_VALUES.
• test_values_test145.m, tests TAU_VALUES.
• test_values_test146.m, tests THERCON_VALUES.
• test_values_test1465.m, tests THREE_J_VALUES.
• test_values_test147.m, tests TRAN02_VALUES.
• test_values_test148.m, tests TRAN03_VALUES.
• test_values_test149.m, tests TRAN04_VALUES.
• test_values_test150.m, tests TRAN05_VALUES.
• test_values_test151.m, tests TRAN06_VALUES.
• test_values_test152.m, tests TRAN07_VALUES.
• test_values_test153.m, tests TRAN08_VALUES.
• test_values_test154.m, tests TRAN09_VALUES.
• test_values_test1545.m, tests TRIGAMMA_VALUES.
• test_values_test155.m, tests TSAT_VALUES.
• test_values_test156.m, tests VAN_DER_CORPUT_VALUES.
• test_values_test157.m, tests VISCOSITY_VALUES.
• test_values_test1575.m, tests VON_MISES_CDF_VALUES.
• test_values_test158.m, tests WEIBULL_CDF_VALUES.
• test_values_test159.m, tests ZETA_VALUES.

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