SPHERICAL_HARMONIC
Evaluate Spherical Harmonic Functions

SPHERICAL_HARMONIC is a MATLAB library which evaluates spherical harmonic functions.

Licensing:

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

Related Data and Programs:

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

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

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

Reference:

1. Milton Abramowitz, Irene Stegun,
   Handbook of Mathematical Functions,
   National Bureau of Standards, 1964,
   ISBN: 0-486-61272-4,
   LC: QA47.A34.
2. Theodore Chihara,
   An Introduction to Orthogonal Polynomials,
   Gordon and Breach, 1978,
   ISBN: 0677041500,
   LC: QA404.5 C44.
3. Walter Gautschi,
   Orthogonal Polynomials: Computation and Approximation,
   Oxford, 2004,
   ISBN: 0-19-850672-4,
   LC: QA404.5 G3555.
4. Eric Weisstein,
   CRC Concise Encyclopedia of Mathematics,
   CRC Press, 2002,
   Second edition,
   ISBN: 1584883472,
   LC: QA5.W45
5. Stephen Wolfram,
   The Mathematica Book,
   Fourth Edition,
   Cambridge University Press, 1999,
   ISBN: 0-521-64314-7,
   LC: QA76.95.W65.
6. Shanjie Zhang, Jianming Jin,
   Computation of Special Functions,
   Wiley, 1996,
   ISBN: 0-471-11963-6,
   LC: QA351.C45.

Source Code:

• legendre_associated_normalized.m, evaluates the associated Legendre functions P(N,M)(X), normalized for use in spherical harmonic calculations;
• legendre_associated_normalized_values.m returns values of the normalized associated Legendre functions.
• r8_factorial.m, computes the (real) factorial function;
• spherical_harmonic.m, evaluates the spherical harmonic function;
• spherical_harmonic_values.m, returns some values of the spherical harmonic function;
• timestamp.m, prints the current YMDHMS date as a timestamp;

Examples and Tests:

• spherical_harmonic_test.m, runs all the tests;
• spherical_harmonic_test_output.txt, is the output from the tests;
• spherical_harmonic_test01.m, tests LEGENDRE_ASSOCIATED_NORMALIZED.
• spherical_harmonic_test02.m, tests SPHERICAL_HARMONIC and SPHERICAL_HARMONIC_VALUES.

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