POLPAK
Recursive Polynomials


POLPAK is a FORTRAN90 library which evaluates a variety of mathematical functions.

It includes routines to evaluate the recursively defined polynomial families of

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 and a Python version

Related Data and Programs:

BERNSTEIN_POLYNOMIAL, a FORTRAN90 library which evaluates the Bernstein polynomials;

CHEBYSHEV_POLYNOMIAL, a FORTRAN90 library which evaluates the Chebyshev polynomial and associated functions.

CLAUSEN, a FORTRAN90 library which evaluates a Chebyshev interpolant to the Clausen function Cl2(x).

CORDIC, a FORTRAN90 library which uses the CORDIC method to compute certain elementary functions.

FN, a FORTRAN90 library which evaluates elementary and special functions, by Wayne Fullerton.

GEGENBAUER_POLYNOMIAL, a FORTRAN90 library which evaluates the Gegenbauer polynomial and associated functions.

HERMITE_POLYNOMIAL, a FORTRAN90 library which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.

JACOBI_POLYNOMIAL, a FORTRAN90 library which evaluates the Jacobi polynomial and associated functions.

LAGUERRE_POLYNOMIAL, a FORTRAN90 library which evaluates the Laguerre polynomial, the generalized Laguerre polynomials, and the Laguerre function.

LEGENDRE_POLYNOMIAL, a FORTRAN90 library which evaluates the Legendre polynomial and associated functions.

LEGENDRE_PRODUCT_POLYNOMIAL, a FORTRAN90 library which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.

LOBATTO_POLYNOMIAL, a FORTRAN90 library which evaluates Lobatto polynomials, similar to Legendre polynomials except that they are zero at both endpoints.

SPECIAL_FUNCTIONS, a FORTRAN90 library which computes the Beta, Error, Gamma, Lambda, Psi functions, the Airy, Bessel I, J, K and Y, Hankel, Jacobian elliptic, Kelvin, Mathieu, Struve functions, spheroidal angular functions, parabolic cylinder functions, hypergeometric functions, the Bernoulli and Euler numbers, the Hermite, Laguerre and Legendre polynomials, the cosine, elliptic, exponential, Fresnel and sine integrals, by Shanjie Zhang, Jianming Jin;

TEST_VALUES, a FORTRAN90 library which contains a few test values of many functions.

Reference:

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    Handbook of Mathematical Functions,
    National Bureau of Standards, 1964,
    ISBN: 0-486-61272-4,
    LC: QA47.A34.
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    Lonesum (0,1)-matrices and poly-Bernoulli numbers of negative index,
    Master of Science Thesis,
    Computer Science Department,
    Iowa State University, 2005.
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    Volume 12, Number 4, December 1986, pages 362-376.
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    ISBN: 0-19-850672-4,
    LC: QA404.5 G3555.
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    A More Symmetrical Fourier Analysis Applied to Transmission Problems,
    Proceedings of the Institute of Radio Engineers,
    Volume 30, 1942, pages 144-150.
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    The Vibonacci Numbers,
    American Scientist,
    Volume 87, Number 4, July-August 1999, pages 296-301.
  14. Brian Hayes,
    Why W?,
    American Scientist,
    Volume 93, Number 2, March-April 2005, pages 104-108.
  15. Ted Hill,
    The First Digit Phenomenon,
    American Scientist,
    Volume 86, Number 4, July/August 1998, pages 358-363.
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    Goedel, Escher, Bach,
    Basic Books, 1979,
    ISBN: 0465026567,
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    Journal Theorie des Nombres Bordeaux,
    Volume 9, Number 1, 1997, pages 221-228.
  18. Cleve Moler,
    Trigonometry is a Complex Subject,
    MATLAB News and Notes, Summer 1998.
  19. Thomas Osler,
    Cardan Polynomials and the Reduction of Radicals,
    Mathematics Magazine,
    Volume 74, Number 1, February 2001, pages 26-32.
  20. J Simoes Pereira,
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    Communications of the ACM,
    Volume 7, Number 7, July 1964, page 420.
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    Second Edition,
    McGraw Hill, 2003,
    ISBN: 0072943505,
    LC: QA162.P56.
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    Scientific American,
    December 1969, pages 109-119.
  23. Dennis Stanton, Dennis White,
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    Springer, 1986,
    ISBN: 0387963472,
    LC: QA164.S79.
  24. Gabor Szego,
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    ISBN: 0821810235,
    LC: QA3.A5.v23.
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    ISBN: 0412993910,
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    LC: QA5.W45
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    Fourth Edition,
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    ACM Algorithm 160: Combinatorial of M Things Taken N at a Time,
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    Wiley, 1996,
    ISBN: 0-471-11963-6,
    LC: QA351.C45.
  32. Daniel Zwillinger, editor,
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    30th Edition,
    CRC Press, 1996,
    ISBN: 0-8493-2479-3,
    LC: QA47.M315.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.


Last revised on 04 November 2013.