Identities for families of orthogonal polynomials and special functions

Integral Transforms and Special Functions

Volumn 5, Issue 1-2, 1997, Pages 69-102

  Koepf, Wolfram ^a  

^a ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

Algorithmical approaches; Orthogonal polynomials; Whittaker functions

Indexed keywords

EID: 0031501905     PISSN: 10652469     EISSN: None     Source Type: Journal    
DOI: 10.1080/10652469708819127     Document Type: Article

References (39)

1. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions. Dover Publ., New York, 1964.
2. R. Askey, Dual equations and classical orthogonal polynomials, J. Math. Anal. Appl. 24 (1968), 677-685.
3. R. Askey and G. Gasper, Jacobi polynomial expansions of Jacobi polynomials with non-negative coefficients, Proc. Camb. Phil. Soc. 70 (1971), 243-255.
4. H. Bateman, The k-function, a particular case of the confluent hypergeometric function, Trans. Amer. Math. Soc. 33(1931), 817-831.
5. Th. Becker and V. Weispfenning, it Gröbner bases. A computational approach to commutative algebra, Springer, New York, 1991.
6. C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral methods in fluid dynamics, Springer Series in Computational Physics, New York-Berlin, 1988.
7. F. Chyzak, Holonomic systems and automatic proofs of identities, Rapport de Recherche 2371, INRIA Research Report, Rocquencourt, 1994, available via anonymous ftp on ftp.inria.fr.
8. P. Deuflhard and M. Wulkow, Computational treatment of polyreaction kinetics by orthogonal polynomials of a discrete variable, IMPACT 1, 1989, 269-301.
9. A. Erdélyi, Higher transcendental functions, 2, McGraw Hill Book Co., Inc., New York, 1953.
10. J. Fleischer, O.V. Tarasov, Calculation of Feynman diagrams from their small momentum expansion, Z. Phys. C64, 1994, 413.
11. J. Fröhlich, Parameter derivatives of the Jacobi polynomials and the Gaussian hypergeometric function, Integral Transforms and Special Functions 2, 1994, 252-266.
12. A.C. Hearn, REDUCE User's Manual, Version 3.6. RAND Co., Santa Monica, CA, 1995.
13. A. Kandri-Rody and V. Weispfenning, Non-commutative Gröbner bases in algebras of soluable type, J. Symbolic Computation 9, 1990, 1-26.
14. W. Koepf, Algorithmic work with orthogonal polynomials and special functions, Konrad-Zuse-Zentrum Berlin (ZIB), Preprint SC 94-5, 1994.
15. W. Koepf, Algorithms for m-fold hypergeometric summation, J. Symbolic Computation, to appear.
16. W. Koepf, REDUCE package for indefinite and definite summation, SIGSAM Bulletin 29, 1995, 14-30.
17. W. Koepf, A MATHEMATICA package on orthogonal polynomials and special functions, in preparation.
18. W. Koepf, Algorithmic Summation and Special Function Identities with Maple, to appear.
19. W. Koepf and D. Schmersau, Bounded nonvanishing functions and Bateman functions, Complex Variables 25, 1994, 237-259.
20. W. Koepf and D. Schmersau, Spaces of functions satisfying simple differential equations, Konrad-Zuse-Zentrum Berlin (ZIB), Technical Report TR 94-2, 1994.
21. T.H. Koornwinder, On Zeilberger's algorithm and its q-analogue: a rigorous description, J. of Comput. and Appl. Math. 48, 1993, 91-111.
22. P. Lesky, Unendliche orthogonale Matrizen und Laguerresche Matrizen, Monatsh. Math. 63, 1958, 59-83.
23. P. Lesky, Die Übersetzung der klassischen orthogonalen Polynome in die Differenzenrechnung, Monatsh. Math. 65, 1961, 1-26.
24. H. Melenk and J. Apel, REDUCE package NCPOLY: Computation in non-commutative polynomial ideals, Konrad-Zuse-Zentrum Berlin (ZIB), 1994.
25. A.F. Nikiforov, S.K. Suslov and V.B. Uvarov, Classical orthogonal polynomials of a discrete variable, Springer-Verlag, Berlin-Heidelberg-New York, 1991.
26. P. Paule and M. Schorn, A MATHEMATICA VERSION OF ZEILBERGER'S ALGORITHM FOR PROVING BINOMIAL COEFFICIENT IDENTITIES, J. Symbolic Computation, to appear 1995.
27. E.D. Rainville, Special functions, The MacMillan Co., New York, 1960.
28. B. Salvy and P. Zimmermann, GFUN: A package for the manipulation of generating and halonomic functions in one variable, ACM Transactions on Mathematical Software 20, 1994, 163-177.
29. R.P. Stanley, Differentiably finite power series, Europ. J. Combinatorics 1, 1980, 175-188.
30. G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Coll. Publ. 23, New York City, 1939.
31. N. Takayama, Gröbner basis and the problem of contiguous relations, Japan J. Appl. Math. 6, 1989, 147-160.
32. N. Takayama, An algorithm of constructing the integral of a module - an infinite dimensional analog of Gröbner basis, Proc. of ISSAC 90, ACM Press, New York, 1990, 206-211.
33. N. Takayama, Gröbner basis, integration and transcendental functions, Proc. of ISSAC 90, ACM Press, New York, 1990, 152-156.
34. F.G. Tricomi, Vorlesungen über Orthogonalreihen, Grundlehren der Mathematischen Wissenschaften, 76, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955.
35. M. Wulkow, Numerical treatment of countable systems of ordinary differential equations, Konrad-Zuse-Zentrum Berlin (ZIB), Technical Report TR 90-8, 1990.
36. D. Zeilberger, A holonomic systems approach to special functions identities, J. Comput. Appl. Math. 32, 1990, 321-368.
37. D. Zeilberger, A fast algorithm for proving terminating hypergeometric identities, Discrete Math. 80, 1990, 207-211.
38. D. Zeilberger, The method of creative telescoping, J. Symbolic Computation 11, 1991, 195-204.
39. D. Zeilberger, Three recitations on holonomic systems and hypergeometric series, Proc. of the 24th Séminaire Lotharingen. Ed. by D. Foata, Publ. I. R. M. A. Strasbourg, 5-37.