On the contiguous relations of hypergeometric series

Journal of Computational and Applied Mathematics

Volumn 192, Issue 2, 2006, Pages 396-410

  Rakha, Medhat A ^a   Ibrahim, Adel K ^a  

^a SUEZ CANAL UNIVERSITY   (Egypt)

Author keywords

Contiguous relations; Hypergeometric function

Indexed keywords

COMPUTATION THEORY; GEOMETRY; MATHEMATICAL MODELS; NUMERICAL METHODS;

CONTIGUOUS RELATIONS; HYPERGEOMETRIC FUNCTION;

POLYNOMIALS;

EID: 33646107616     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.05.016     Document Type: Article

References (11)

1. Andrews G.E., Askey R., and Roy R. Special Functions (1999), Cambridge University Press, Cambridge
2. B. Buchberger, Introduction to Gröbner bases, in: B. Buchberger, F. Winkler (Eds.), Gröbner Bases and Applications, London Mathematical Society Lecture Notes Series, vol. 251, Cambridge University Press, Cambridge, 1998, pp. 3-31.
3. G. Gasper, M. Rahman, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, vol. 35, Cambridge University Press, Cambridge, 1990.
4. Horner L. Hypergeometric Functions: Towards a Generalized Treatment of Contiguous Relations (May 2001), Nebraska Academy of Science
5. Miller Jr. W. Lie theory and generalizations of hypergeometric functions. SIAM J. Appl. Math. 25 (1973) 226-235
6. P. Paule, Contiguous relations and creative telescoping, Technical Report, RISC, Austria, 2001.
7. Rainville E.D. Special Functions (1960), The Macmillan Company, New York
8. Takayama N. Gröbner basis and the problem of contiguous relations. Japan J. Appl. Math. 6 1 (1989) 147-160
9. Takayama N. Algorithm finding recurrence relations of binomial sums and its complexity. J. Symbolic Comput. 20 (1995) 637-651
10. Vidúnas R. A generalization of Kummer's identity. Rocky Mountain J. Math. 32 2 (2002) 919-935
11. Vidúnas R. Contiguous relations of hypergeometric series. J. Math. Anal. Appl. 135 (2003) 507-519