POLPAK
Recursive Polynomials


POLPAK is a C 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.

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 C library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

BESSELJ, a C library which evaluates Bessel J functions of noninteger order.

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

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

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

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

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

TEST_VALUES, a C library which stores values of many mathematical functions, and can be used for testing.

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 Banks,
    Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics,
    Princeton, 1999,
    ISBN13: 9780691059471,
    LC: QA93.B358.
  3. Frank Benford,
    The Law of Anomalous Numbers,
    Proceedings of the American Philosophical Society,
    Volume 78, 1938, pages 551-572.
  4. Paul Bratley, Bennett Fox, Linus Schrage,
    A Guide to Simulation,
    Second Edition,
    Springer, 1987,
    ISBN: 0387964673,
    LC: QA76.9.C65.B73.
  5. Chad Brewbaker,
    Lonesum (0,1)-matrices and poly-Bernoulli numbers of negative index,
    Master of Science Thesis,
    Computer Science Department,
    Iowa State University, 2005.
  6. 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.
  7. Theodore Chihara,
    An Introduction to Orthogonal Polynomials,
    Gordon and Breach, 1978,
    ISBN: 0677041500,
    LC: QA404.5 C44.
  8. William Cody,
    Rational Chebyshev Approximations for the Error Function,
    Mathematics of Computation,
    Volume 23, Number 107, July 1969, pages 631-638.
  9. 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.
  10. 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.
  11. Walter Gautschi,
    Orthogonal Polynomials: Computation and Approximation,
    Oxford, 2004,
    ISBN: 0-19-850672-4,
    LC: QA404.5 G3555.
  12. Ralph Hartley,
    A More Symmetrical Fourier Analysis Applied to Transmission Problems,
    Proceedings of the Institute of Radio Engineers,
    Volume 30, 1942, pages 144-150.
  13. Brian Hayes,
    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.
  16. Douglas Hofstadter,
    Goedel, Escher, Bach,
    Basic Books, 1979,
    ISBN: 0465026567,
    LC: QA9.8H63.
  17. Masanobu Kaneko,
    Poly-Bernoulli Numbers,
    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,
    Algorithm 234: Poisson-Charliers Polynomials,
    Communications of the ACM,
    Volume 7, Number 7, July 1964, page 420.
  21. Charles Pinter,
    A Book of Abstract Algebra,
    Second Edition,
    McGraw Hill, 2003,
    ISBN: 0072943505,
    LC: QA162.P56.
  22. Ralph Raimi,
    The Peculiar Distribution of First Digits,
    Scientific American,
    December 1969, pages 109-119.
  23. Dennis Stanton, Dennis White,
    Constructive Combinatorics,
    Springer, 1986,
    ISBN: 0387963472,
    LC: QA164.S79.
  24. Gabor Szego,
    Orthogonal Polynomials,
    American Mathematical Society, 1992,
    ISBN: 0821810235,
    LC: QA3.A5.v23.
  25. Daniel Velleman, Gregory Call,
    Permutations and Combination Locks,
    Mathematics Magazine,
    Volume 68, Number 4, October 1995, pages 243-253.
  26. Divakar Viswanath,
    Random Fibonacci sequences and the number 1.13198824,
    Mathematics of Computation,
    Volume 69, Number 231, July 2000, pages 1131-1155.
  27. Michael Waterman,
    Introduction to Computational Biology,
    Chapman and Hall, 1995,
    ISBN: 0412993910,
    LC: QH438.4.M33.W38.
  28. Eric Weisstein,
    CRC Concise Encyclopedia of Mathematics,
    CRC Press, 2002,
    Second edition,
    ISBN: 1584883472,
    LC: QA5.W45
  29. Stephen Wolfram,
    The Mathematica Book,
    Fourth Edition,
    Cambridge University Press, 1999,
    ISBN: 0-521-64314-7,
    LC: QA76.95.W65.
  30. 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.
  31. Shanjie Zhang, Jianming Jin,
    Computation of Special Functions,
    Wiley, 1996,
    ISBN: 0-471-11963-6,
    LC: QA351.C45.
  32. Daniel Zwillinger, editor,
    CRC Standard Mathematical Tables and Formulae,
    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 C source codes.


Last revised on 13 May 2014.