The Dynamic Dictionary of Mathematical Functions (DDMF)

  • Alexandre Benoit
  • Frédéric Chyzak
  • Alexis Darrasse
  • Stefan Gerhold
  • Marc Mezzarobba
  • Bruno Salvy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)

Abstract

We describe the main features of the Dynamic Dictionary of Mathematical Functions (version 1.5). It is a website consisting of interactive tables of mathematical formulas on elementary and special functions. The formulas are automatically generated by computer algebra routines. The user can ask for more terms of the expansions, more digits of the numerical values, or proofs of some of the formulas.

References

  1. 1.
    Abramowitz, M., Stegun, I.A. (eds.): Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover Publications Inc., New York (1992); Reprint of the 1972 edition. First edition 1964 Google Scholar
  2. 2.
    Benoit, A., Salvy, B.: Chebyshev expansions for solutions of linear differential equations. In: May, J. (ed.) Symbolic and Algebraic Computation, pp. 23–30. ACM Press, New York (2009); Proceedings of ISSAC 2009, Seoul (July 2009)Google Scholar
  3. 3.
    Boisvert, R., Lozier, D.W.: Handbook of Mathematical Functions. In: A Century of Excellence in Measurements Standards and Technology, pp. 135–139. CRC Press, Boca Raton (2001)Google Scholar
  4. 4.
    Chyzak, F.: Groebner bases, symbolic summation and symbolic integration. In: Buchberger, B., Winkler, F. (eds.) Groebner Bases and Applications, Proc. of the Conference 33 Years of Gröbner Bases. London Mathematical Society Lecture Notes Series, vol. 251, pp. 32–60. Cambridge University Press, Cambridge (1998)Google Scholar
  5. 5.
    Chyzak, F.: An extension of Zeilberger’s fast algorithm to general holonomic functions. Discrete Mathematics 217(1-3), 115–134 (2000)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chyzak, F., Kauers, M., Salvy, B.: A non-holonomic systems approach to special function identities. In: May, J. (ed.) Symbolic and Algebraic Computation, pp. 111–118. ACM Press, New York (2009); Proceedings of ISSAC 2009, Seoul (July 2009) Google Scholar
  7. 7.
    Erdélyi, A.: Higher Transcendental Functions, vol. 1-3. R. E. Krieger Publishing Company, Inc., Malabar (1981); First edition 1953 Google Scholar
  8. 8.
    Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Academic Press, London (1996); First English edition 1965Google Scholar
  9. 9.
    Lipshitz, L.: D-finite power series. Journal of Algebra 122(2), 353–373 (1989)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Meunier, L., Salvy, B.: ESF: An automatically generated encyclopedia of special functions. In: Sendra, J.R. (ed.) Symbolic and Algebraic Computation, pp. 199–205. ACM Press, New York (2003); Proceedings of ISSAC 2003, Philadelphia (August 2003) Google Scholar
  11. 11.
    Mezzarobba, M.: NumGfun: a package for numerical and analytic computation with D-finite functions. In: ISSAC 2010. ACM Press, New York (2010), http://arxiv.org/abs/1002.3077 Google Scholar
  12. 12.
    Mezzarobba, M., Salvy, B.: Effective bounds for P-recursive sequences. Journal of Symbolic Computation (to appear)Google Scholar
  13. 13.
    Olver, F.W.J., Lozier, D.W., Boisvert, R.F., Clark, C.W. (eds.): NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge (2010)MATHGoogle Scholar
  14. 14.
    Petkovšek, M.: Hypergeometric solutions of linear recurrences with polynomial coefficients. Journal of Symbolic Computation 14(2-3), 243–264 (1992)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I.: Integrals and Series, 1st edn. in Moscow, Nauka, vol. 1-6 (1981)Google Scholar
  16. 16.
    Salvy, B., Zimmermann, P.: Gfun: a Maple package for the manipulation of generating and holonomic functions in one variable. ACM Transactions on Mathematical Software 20(2), 163–177 (1994)MATHCrossRefGoogle Scholar
  17. 17.
    Stanley, R.P.: Differentiably finite power series. European Journal of Combinatorics 1(2), 175–188 (1980)MATHMathSciNetGoogle Scholar
  18. 18.
    Zeilberger, D.: A holonomic systems approach to special functions identities. Journal of Computational and Applied Mathematics 32(3), 321–368 (1990)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alexandre Benoit
    • 1
  • Frédéric Chyzak
    • 1
  • Alexis Darrasse
    • 1
  • Stefan Gerhold
    • 1
  • Marc Mezzarobba
    • 1
  • Bruno Salvy
    • 1
  1. 1.Inria Paris-RocquencourtFrance

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