POLPAK
Recursive Polynomials

POLPAK is a MATLAB library which evaluates a variety of mathematical functions.

It includes routines to evaluate the recursively defined polynomial families of

Bernoulli
Bernstein
Cardan
Charlier
Chebyshev
Euler
Gegenbauer
Hermite
Jacobi
Krawtchouk
Laguerre
Legendre
Meixner
Zernike

A variety of other polynomials and functions have been added. In a few cases, the new recursive feature of FORTRAN90 has been used (but NOT for the factorial function!)

Licensing:

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

Languages:

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

Related Data and Programs:

BERNSTEIN, a MATLAB library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

CHEBYSHEV_POLYNOMIAL, a MATLAB library which evaluates the Chebyshev polynomial and associated functions.

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.

HERMITE_POLYNOMIAL, a MATLAB library which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.

JACOBI_POLYNOMIAL, a MATLAB library which evaluates the Jacobi polynomial and associated functions.

LAGUERRE_POLYNOMIAL, a MATLAB library which evaluates the Laguerre polynomial, the generalized Laguerre polynomial, and the Laguerre function.

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

SPHERICAL_HARMONIC, a MATLAB library which evaluates spherical harmonic functions.

TEST_VALUES, a MATLAB library which contains some sample values of many mathematical functions.

Reference:

Milton Abramowitz, Irene Stegun,
Handbook of Mathematical Functions,
National Bureau of Standards, 1964,
ISBN: 0-486-61272-4,
LC: QA47.A34.
Robert Banks,
Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics,
Princeton, 1999,
ISBN13: 9780691059471,
LC: QA93.B358.
Frank Benford,
The Law of Anomalous Numbers,
Proceedings of the American Philosophical Society,
Volume 78, 1938, pages 551-572.
Paul Bratley, Bennett Fox, Linus Schrage,
A Guide to Simulation,
Second Edition,
Springer, 1987,
ISBN: 0387964673,
LC: QA76.9.C65.B73.
Chad Brewbaker,
Lonesum (0,1)-matrices and poly-Bernoulli numbers of negative index,
Master of Science Thesis,
Computer Science Department,
Iowa State University, 2005.
William Briggs, Van Emden Henson,
The DFT: An Owner's Manual for the Discrete Fourier Transform,
SIAM, 1995,
ISBN13: 978-0-898713-42-8,
LC: QA403.5.B75.
Theodore Chihara,
An Introduction to Orthogonal Polynomials,
Gordon and Breach, 1978,
ISBN: 0677041500,
LC: QA404.5 C44.
William Cody,
Rational Chebyshev Approximations for the Error Function,
Mathematics of Computation,
Volume 23, Number 107, July 1969, pages 631-638.
Robert Corless, Gaston Gonnet, David Hare, David Jeffrey, Donald Knuth,
On the Lambert W Function,
Advances in Computational Mathematics,
Volume 5, Number 1, December 1996, pages 329-359.
Bennett Fox,
Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators,
ACM Transactions on Mathematical Software,
Volume 12, Number 4, December 1986, pages 362-376.
Walter Gautschi,
Orthogonal Polynomials: Computation and Approximation,
Oxford, 2004,
ISBN: 0-19-850672-4,
LC: QA404.5 G3555.
Ralph Hartley,
A More Symmetrical Fourier Analysis Applied to Transmission Problems,
Proceedings of the Institute of Radio Engineers,
Volume 30, 1942, pages 144-150.
Brian Hayes,
The Vibonacci Numbers,
American Scientist,
Volume 87, Number 4, July-August 1999, pages 296-301.
Brian Hayes,
Why W?,
American Scientist,
Volume 93, Number 2, March-April 2005, pages 104-108.
Ted Hill,
The First Digit Phenomenon,
American Scientist,
Volume 86, Number 4, July/August 1998, pages 358-363.
Douglas Hofstadter,
Goedel, Escher, Bach,
Basic Books, 1979,
ISBN: 0465026567,
LC: QA9.8H63.
Masanobu Kaneko,
Poly-Bernoulli Numbers,
Journal Theorie des Nombres Bordeaux,
Volume 9, Number 1, 1997, pages 221-228.
Cleve Moler,
Trigonometry is a Complex Subject,
MATLAB News and Notes, Summer 1998.
Thomas Osler,
Cardan Polynomials and the Reduction of Radicals,
Mathematics Magazine,
Volume 74, Number 1, February 2001, pages 26-32.
J Simoes Pereira,
Algorithm 234: Poisson-Charliers Polynomials,
Communications of the ACM,
Volume 7, Number 7, July 1964, page 420.
Charles Pinter,
A Book of Abstract Algebra,
Second Edition,
McGraw Hill, 2003,
ISBN: 0072943505,
LC: QA162.P56.
Ralph Raimi,
The Peculiar Distribution of First Digits,
Scientific American,
December 1969, pages 109-119.
Dennis Stanton, Dennis White,
Constructive Combinatorics,
Springer, 1986,
ISBN: 0387963472,
LC: QA164.S79.
Gabor Szego,
Orthogonal Polynomials,
American Mathematical Society, 1992,
ISBN: 0821810235,
LC: QA3.A5.v23.
Daniel Velleman, Gregory Call,
Permutations and Combination Locks,
Mathematics Magazine,
Volume 68, Number 4, October 1995, pages 243-253.
Divakar Viswanath,
Random Fibonacci sequences and the number 1.13198824,
Mathematics of Computation,
Volume 69, Number 231, July 2000, pages 1131-1155.
Michael Waterman,
Introduction to Computational Biology,
Chapman and Hall, 1995,
ISBN: 0412993910,
LC: QH438.4.M33.W38.
Eric Weisstein,
CRC Concise Encyclopedia of Mathematics,
CRC Press, 2002,
Second edition,
ISBN: 1584883472,
LC: QA5.W45
Stephen Wolfram,
The Mathematica Book,
Fourth Edition,
Cambridge University Press, 1999,
ISBN: 0-521-64314-7,
LC: QA76.95.W65.
ML Wolfson, HV Wright,
ACM Algorithm 160: Combinatorial of M Things Taken N at a Time,
Communications of the ACM,
Volume 6, Number 4, April 1963, page 161.
Shanjie Zhang, Jianming Jin,
Computation of Special Functions,
Wiley, 1996,
ISBN: 0-471-11963-6,
LC: QA351.C45.
Daniel Zwillinger, editor,
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30th Edition,
CRC Press, 1996,
ISBN: 0-8493-2479-3,
LC: QA47.M315.

Source Code:

agm.m, computes the arithmetic geometric mean of two numbers;
agud.m, evaluates the inverse Gudermannian function;
align_enum.m, counts the alignments of two sequences of M and N elements;
arc_cosine.m, computes the inverse cosine of a value, with argument truncation;
arc_sine.m, computes the inverse sine of a value, with argument truncation;
asinh2.m, computes the inverse hyperbolic sine of a value;
atan4.m, computes the inverse tangent of the ratio Y / X;
atanh2.m, computes the inverse hyperbolic tangent of a value;
bell.m, evaluates the Bell numbers;
bell_values.m, evaluates some values of the Bell numbers;
benford.m, returns the Benford probability of one or more significant digits;
bernoulli_number.m, returns the Bernoulli numbers;
bernoulli_number2.m, returns the Bernoulli numbers;
bernoulli_number3.m, computes the Bernoulli numbers;
bernoulli_number_values.m, returns some values of the Bernoulli numbers;
bernoulli_poly.m, evaluates a Bernoulli polynomial;
bernoulli_poly2.m, evaluates the Nth Bernoulli polynomial at X;
bernstein_poly.m, evaluates the Bernstein polynomials at a point;
bernstein_poly_values.m, returns some values of the Bernstein polynomials;
beta.m, evaluates the Beta function;
beta_values.m, returns some values of the Beta function;
bpab.m, evaluates the Bernstein polynomials defined on the interval [A,B];
cardan.m, evaluates the Cardan polynomials;
cardan_poly_coef.m, returns the coefficients of a Cardan polynomial;
catalan.m, evaluates the Catalan numbers;
catalan_row_next.m, computes the next row of Catalan numbers;
catalan_values.m, evaluates some values of the Catalan numbers;
charlier.m, evaluates the Charlier polynomials;
cheby_t_poly.m, evaluates the Chebyshev T polynomials;
cheby_t_poly_coef.m, returns the coefficients of the Chebyshev T polynomials;
cheby_t_values.m, returns some values of the Chebyshev T polynomials;
cheby_t_poly_zero.m, returns the zeros of the Chebyshev T polynomials;
cheby_u_poly.m, evaluates the Chebyshev U polynomials;
cheby_u_poly_coef.m, returns the coefficients of the Chebyshev U polynomials;
cheby_u_values.m, returns some values of the Chebyshev U polynomials;
cheby_u_poly_zero.m, returns the zeros of the Chebyshev U polynomials;
chebyshev_discrete.m, evaluates the discrete Chebyshev polynomials;
collatz_count.m, counts the length of the Collatz sequence for a seed of N;
collatz_count_max.m, seeks the maximum Collatz count from 1 to N.
collatz_count_values.m, stores some values of the Collatz count function;
comb_row.m, computes row N of Pascal's triangle;
commul.m, computes a multinomial coefficient;
cos_deg.m, computes the cosine of an angle given in degrees;
cos_power_int.m, returns the value of the integral of the N-th power of the cosine function;
cos_power_int_values.m, returns some values of the integral of the N-th power of the cosine function;
delannoy.m, computes the Delannoy numbers;
e_constant.m, returns the value of the base of the natural logarithm system;
erf_values.m, returns some values of the error function;
error_f.m, evaluates the error function ERF(X);
error_f_inverse.m, inverts the error function ERF(X);
euler_constant.m, returns the value of the Euler-Mascheroni constant;
euler_number.m, evaluates the Euler numbers;
euler_number2.m, computes the Euler numbers;
euler_number_values.m, returns some values of the Euler numbers;
euler_poly.m, evaluates the N-th Euler polynomial at X;
eulerian.m, computes the eulerian number E(N,K);
f_hofstadter.m, computes the Hofstadter F function;
fibonacci_direct.m, computes the N-th Fibonacci number directly;
fibonacci_floor.m, computes the largest Fibonacci number less than or equal to N;
fibonacci_recursive.m, computes the first N Fibonacci numbers recursively;
g_hofstadter.m, computes the Hofstadter G function;
gamma_values.m, returns some values of the Gamma function;
gamma_log_values.m, returns some values of the logarithm of the Gamma function;
gegenbauer_poly.m, evaluates the Gegenbauer polynomials at a point;
gegenbauer_values.m, returns some values of the Gegenbauer polynomials;
gen_hermite_poly.m, evaluates the generalized Hermite polynomials;
gen_laguerre_poly.m, evaluates the generalized Laguerre polynomials;
gud.m, evaluates the Gudermannian function;
gud_values.m, returns some values of the Gudermannian function;
h_hofstadter.m, computes the Hofstadter H function;
hail.m, computes the hail function;
hermite_poly.m, evaluates the Hermite polynomials;
hermite_poly_coef.m, evaluates the Hermite polynomial coefficients;
hermite_poly_values.m, returns some values of the Hermite polynomials;
hyper_2f1_values.m, returns some values of the 2F1 hypergeometric function.
i4_choose.m, computes the combinatorial coefficient C(N,K);
i4_factor.m, factors an integer into prime factors;
i4_factorial.m, computes N! for small values of N;
i4_factorial_values.m, returns some values of the (integer) factorial function;
i4_factorial2.m, computes the double factorial function;
i4_factorial2_values.m, returns some values of the double factorial function;
i4_is_prime.m, determines whether an integer is prime;
i4_is_triangular.m, determines whether an integer is triangular;
i4_partition_distinct_count_values.m, computes the value of Q(N);
i4_pochhammer.m, returns the value of I*(I+1)*...*(J-1)*J;
i4_swap.m, swaps two integer values;
i4_to_triangle.m, converts an integer to triangular coordinates;
i4_uniform.m, returns a random integer in a given range;
i4mat_print.m, prints an I4MAT;
i4mat_print_some.m, prints some of an I4MAT;
jacobi_poly.m, evaluates the Jacobi polynomials at a point;
jacobi_poly_values.m, returns some values of the Jacobi polynomials;
jacobi_symbol.m, evaluates the Jacobi symbol (Q/P);
krawtchouk.m, evaluates the Krawtchouk polynomials;
laguerre_associated.m, evaluates the associated Laguerre polynomials L(N,M)(X);
laguerre_poly.m, evaluates the Laguerre polynomials;
laguerre_poly_coef.m, evaluates the Laguerre polynomial coefficients;
laguerre_polynomial_values.m, returns some values of the Laguerre polynomials;
legendre_associated.m, evaluates the associated Legendre functions P(N,M)(X);
legendre_associated_normalized.m, evaluates the associated Legendre functions P(N,M)(X), normalized for use in spherical harmonic calculations;
legendre_associated_values.m, returns some values of the associated Legendre function;
legendre_function_q.m, evaluates the Legendre functions Q(N)(X);
legendre_function_q_values.m, returns some values of the Legendre Q(N) functions;
legendre_poly.m, evaluates the Legendre polynomials P(N)(X);
legendre_poly_coef.m, evaluates the coefficients of the Legendre polynomials P(N)(X);
legendre_poly_values.m, returns some values of the Legendre polynomials;
legendre_symbol.m, evaluates the Legendre symbol (Q/P);
lerch.m, evaluates the Lerch transcendent function;
lerch_values.m, returns some values of the Lerch transcendent function;
lock.m, returns the number of codes for a lock with N buttons;
meixner.m, evaluates the Meixner polynomials;
mertens.m, returns the value of the Mertens function;
mertens_values.m, returns some tabulated values of the Mertens function;
moebius.m, returns the value of MU(N), the Moebius function of N;
moebius_values.m, returns some tabulated values of the Moebius function;
motzkin.m, returns the Motzkin numbers up to order N;
normal_01_cdf_inv.m inverts the Normal 01 CDF.
omega.m, returns the number of distinct prime divisors of an integer;
omega_values.m, returns some values of the Omega function;
partition_count_values.m, returns some values of the integer partition count;
partition_distinct_count_values.m, returns some values of Q(N);
pentagon_num.m, returns the N-th pentagonal number;
phi.m, returns the number of relatively prime predecessors of an integer;
phi_values.m, returns some values of the Phi function;
poly_bernoulli.m, evaluates the poly-Bernoulli numbers of negative index;
poly_coef_count.m, counts the coefficients in a polynomial of given degree and dimension.
prime.m, returns any of the first MAXPRIME primes;
psi_values.m, returns some values of the Psi function;
pyramid_num.m, returns the N-th pyramidal number;
r4_uniform_01.m, returns a unit pseudorandom R4;
r8_acosh.m, computes the inverse hyperbolic cosine of a value;
r8_asinh.m, computes the inverse hyperbolic sine of a value;
r8_atanh.m, computes the inverse hyperbolic tangent of a value;
r8_choose.m, computes the combinatorial coefficient C(N,K);
r8_cot.m, computes the cotangent of an angle;
r8_cot_deg.m, computes the cotangent of an angle given in degrees;
r8_csc.m, computes the cosecant of an angle;
r8_csc_deg.m, computes the cosecant of an angle given in degrees;
r8_epsilon.m, returns the R8 machine precision;
r8_factorial.m, computes the (real) factorial function;
r8_factorial_log.m, computes the logarithm of the (real) factorial function;
r8_factorial_log_values.m, returns some values of the logarithm of the (real) factorial function;
r8_factorial_values.m, returns some values of the (real) factorial function;
r8_gamma.m, returns the Gamma function;
r8_gamma_log.m, returns the logarithm of the Gamma function;
r8_huge.m, returns a "huge" value;
r8_hyper_2f1.m, evaluates the 2F1 hypergeometric function.
r8_nint.m, rounds an R8 to the nearest integer;
r8_pi.m, returns the value of Pi;
r8_psi.m, returns the Psi function;
r8_uniform_01.m, returns a unit pseudorandom R8;
r8poly_degree.m, returns the degree of a polynomial;
r8poly_print.m, prints a polynomial;
r8poly_val_horner.m, evaluates a polynomial using Horner's method;
r8poly_value.m, evaluates a polynomial using Horner's method;
s_len_trim.m, returns the length of a string to the last nonblank;
sec_deg.m, computes the secant of an angle given in degrees;
sigma.m, returns the value of SIGMA(N), the divisor sum;
sigma_values.m, returns some values of the Sigma function;
sin_deg.m, computes the sin of an angle given in degrees;
sin_power_int.m, returns the value of the integral of the N-th power of the sine function;
sin_power_int_values.m, returns some values of the integral of the N-th power of the sine function;
slice.m, maximum number of pieces created by a given number of slices.
spherical_harmonic.m, evaluates the spherical harmonic function;
spherical_harmonic_values.m, returns some values of the spherical harmonic function;
stirling1.m, returns the Stirling numbers of the first kind;
stirling2.m, returns the Stirling numbers of the second kind;
tan_deg.m, returns the tangent of an angle given in degrees;
tau.m, evaluates the Tau function, the number of distinct divisors;
tau_values.m, returns some values of the Tau function;
tetrahedron_num.m, returns the N-th tetrahedral number;
timestamp.m, prints the current YMDHMS date as a timestamp;
triangle_num.m, returns the N-th triangle number;
triangle_to_i4.m, converts a triangular coordinate to an integer;
v_hofstadter.m, computes the Hofstadter V function;
vibonacci.m, computes the Vibonacci numbers;
zeckendorf.m, produces the Zeckendorf decomposition of a positive integer;
zernike_poly.m, evaluates a Zernike polynomial;
zernike_poly_coef.m, returns the coefficients of a Zernike polynomial;
zeta.m, approximates the Riemann Zeta function;
zeta_values.m, returns some stored values of the Riemann Zeta function;

Examples and Tests:

polpak_test.m, runs all the tests;
polpak_test_output.txt, is the output from the tests;
polpak_test001.m, tests AGM;
polpak_test002.m, tests AGUD and GUD;
polpak_test003.m, tests ALIGN_ENUM;
polpak_test0035.m, tests ARC_COSINE;
polpak_test004.m, tests ASINH2;
polpak_test005.m, tests ATAN4;
polpak_test006.m, tests ATANH2;
polpak_test007.m, tests BELL and BELL_VALUES;
polpak_test008.m, tests BENFORD;
polpak_test010.m, tests BERNOULLI_NUMBER and BERNOULLI_NUMBER_VALUES;
polpak_test0102.m, tests BERNOULLI_NUMBER2 and BERNOULLI_NUMBER_VALUES;
polpak_test0104.m, tests BERNOULLI_NUMBER3 and BERNOULLI_NUMBER_VALUES;
polpak_test011.m, tests BERNOULLI_POLY;
polpak_test0115.m, tests BERNOULLI_POLY2;
polpak_test012.m, tests BETA and BETA_VALUES;
polpak_test013.m, tests BERNSTEIN_POLY and BERNSTEIN_POLY_VALUES;
polpak_test014.m, tests BPAB;
polpak_test015.m, tests CARDAN and CARDAN_POLY_COEF;
polpak_test016.m, tests CATALAN and CATALAN_VALUES;
polpak_test017.m, tests CATALAN_ROW;
polpak_test0175.m, tests CHARLIER;
polpak_test018.m, tests CHEBY_T_POLY and CHEBY_T_POLY_VALUES;
polpak_test0185.m, tests CHEBY_T_POLY_ZERO;
polpak_test019.m, tests CHEBY_T_POLY_COEF;
polpak_test020.m, tests CHEBY_U_POLY and CHEBY_U_POLY_VALUES;
polpak_test021.m, tests CHEBY_U_POLY_COEF;
polpak_test0215.m, tests CHEBY_U_POLY_ZERO;
polpak_test0216.m, tests CHEBYSHEV_DISCRETE;
polpak_test0217.m, tests COLLATZ_COUNT and COLLATZ_COUNT_VALUES;
polpak_test0218.m, tests COLLATZ_COUNT_MAX;
polpak_test024.m, tests COMB_ROW;
polpak_test0243.m, tests COS_POWER_INT and COS_POWER_INT_VALUES;
polpak_test01155.m, tests DELANNOY;
polpak_test0116.m, tests ERROR_F and ERF_VALUES;
polpak_test0245.m, tests R8_FACTORIAL and R8_FACTORIAL_VALUES;
polpak_test025.m, tests ERF and ERF_VALUES;
polpak_test0255.m, tests ERF_INVERSE and ERF_VALUES;
polpak_test026.m, tests EULER_NUMBER and EULER_NUMBER_VALUES;
polpak_test0265.m, tests EULER_NUMBER2 and EULER_NUMBER_VALUES;
polpak_test028.m, tests EULER_POLY;
polpak_test027.m, tests EULERIAN;
polpak_test029.m, tests F_HOFSTADTER;
polpak_test031.m, tests FIBONACCI_DIRECT;
polpak_test032.m, tests FIBONACCI_FLOOR;
polpak_test033.m, tests FIBONACCI_RECURSIVE;
polpak_test034.m, tests G_HOFSTADTER;
polpak_test036.m, tests GAMMA_LOG and GAMMA_LOG_VALUES;
polpak_test037.m, tests GEGENBAUER_POLY and GEGENBAUER_VALUES;
polpak_test038.m, tests GUD and GUD_VALUES;
polpak_test039.m, tests HAIL;
polpak_test040.m, tests H_HOFSTADTER;
polpak_test041.m, tests HERMITE_POLY and HERMITE_POLY_VALUES;
polpak_test042.m, tests HERMITE_POLY_COEF;
polpak_test0425.m, tests R8_HYPER_2F1;
polpak_test023.m, tests I4_CHOOSE;
polpak_test043.m, tests I4_FACTORIAL and I4_FACTORIAL_VALUES;
polpak_test044.m, tests I4_FACTORIAL2 and I4_FACTORIAL2_VALUES;
polpak_test045.m, tests PARTITION_COUNT_VALUES;
polpak_test046.m, tests I4_PARTITION_DISTINCT_COUNT and PARTITION_DISTINCT_COUNT_VALUES;;
polpak_test047.m, tests I4_POCHHAMMER;
polpak_test048.m, tests I4_TO_TRIANGLE, TRIANGLE_TO_I4 and I4_IS_TRIANGULAR;
polpak_test049.m, tests JACOBI_POLY and JACOBI_POLY_VALUES;
polpak_test050.m, tests JACOBI_SYMBOL;
polpak_test0505.m, tests KRAWTCHOUK;
polpak_test051.m, tests LAGUERRE_ASSOCIATED;
polpak_test052.m, tests GEN_LAGUERRE_POLY;
polpak_test054.m, tests LAGUERRE_POLY and LAGUERRE_POLYNOMIAL_VALUES;
polpak_test055.m, tests LAGUERRE_POLY_COEF;
polpak_test057.m, tests LEGENDRE_POLY and LEGENDRE_POLY_VALUES;
polpak_test058.m, tests LEGENDRE_POLY_COEF;
polpak_test059.m, tests LEGENDRE_ASSOCIATED and LEGENDRE_ASSOCIATED_VALUES;
polpak_test0595.m, tests LEGENDRE_ASSOCIATED_NORMALIZED and LEGENDRE_ASSOCIATED_NORMALIZED_VALUES;
polpak_test060.m, tests LEGENDRE_FUNCTION_Q and LEGENDRE_FUNCTION_Q_VALUES;
polpak_test061.m, tests LEGENDRE_SYMBOL;
polpak_test0615.m, tests LERCH and LERCH_VALUES;
polpak_test062.m, tests LOCK;
polpak_test0623.m, tests MEIXNER;
polpak_test0625.m, tests MERTENS and MERTENS_VALUES;
polpak_test063.m, tests MOEBIUS and MOEBIUS_VALUES;
polpak_test0635.m, tests MOTZKIN;
polpak_test064.m, tests OMEGA and OMEGA_VALUES;
polpak_test065.m, tests PENTAGON_NUM;
polpak_test066.m, tests PHI and PHI_VALUES;
polpak_test0665.m, tests POLY_BERNOULLI;
polpak_test0667.m, tests POLY_COEF_COUNT;
polpak_test067.m, tests PYRAMID_NUM;
polpak_test0675.m, tests R8_ACOSH2;
polpak_test068.m, tests R8_FACTORIAL and R8_FACTORIAL_VALUES;
polpak_test022.m, tests R8_CHOOSE;
polpak_test0685.m, tests R8_FACTORIAL_LOG and R8_FACTORIAL_LOG_VALUES;
polpak_test06855.m, tests R8_GAMMA and GAMMA_VALUES;
polpak_test06856.m, tests R8_PSI and PSI_VALUES;
polpak_test069.m, tests SIGMA and SIGMA_VALUES;
polpak_test0695.m, tests SIN_POWER_INT and SIN_POWER_INT_VALUES;
polpak_test0696.m, tests SLICE;
polpak_test0697.m, tests SPHERICAL_HARMONIC and SPHERICAL_HARMONIC_VALUES;
polpak_test070.m, tests STIRLING1;
polpak_test071.m, tests STIRLING2;
polpak_test072.m, tests TAU and TAU_VALUES;
polpak_test073.m, tests TETRAHEDRON_NUM;
polpak_test074.m, tests TRIANGLE_NUM;
polpak_test075.m, tests V_HOFSTADTER;
polpak_test076.m, tests VIBONACCI;
polpak_test077.m, tests ZECKENDORF;
polpak_test0773.m, tests ZERNIKE_POLY;
polpak_test0775.m, tests ZERNIKE_POLY_COEF;
polpak_test078.m, tests ZETA and ZETA_VALUES;

You can go up one level to the MATLAB source codes.

Last revised on 12 August 2011.