Reduction formulas for Karlsson-Minton-type hypergeometric functions

Constructive Approximation

Volumn 20, Issue 4, 2004, Pages 525-548

  Rosengren, Hjalmar ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Hypergeometric series on root systems; Karlsson Minton type hypergeometric series

Indexed keywords

EID: 4644229153     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00365-003-0541-6     Document Type: Article

References (30)

1. 6. Proc. Amer. Math. Soc., 77:218-222.
2. W. N. BAILEY (1929): An identity involving Heine's basic hypergeometric series. J. London Math. Soc., 4:254-257.
3. 3. Quart. J. Math. Oxford Ser. (2), 10:92-94.
4. G. BHATNAGAR (1995): Inverse relations, generalized bibasic series and their U(n) extensions. PhD dissertation. Ohio State University..
5. W. CHU (1998): Partial-fraction expansions and well-poised bilateral series. Acta Sci. Math. (Szeged), 64:495-513.
6. R. Y. DENIS, R. A. GUSTAFSON (1992): An SU(n) q-beta integral transformation and multiple hypergeometric series identities. SIAM J. Math. Anal., 23:552-561.
7. J. L. FIELDS, J. WIMP (1961): Expansions of hypergeometric functions in hypergeometric functions. Math. Comp., 15:390-395.
8. C. Fox (1927): The expression of hypergeometric series in terms of similar series. Proc. London Math. Soc. (2), 26:201-210.
9. G. GASPER (1981): Summation formulas for basic hypergeometric series. SIAM J. Math. Anal., 12:196-200.
10. G. GASPER (1997): Elementary derivations of summation and transformation formulas for q-series. In: Special Functions, q-Series and Related Topics. Fields Inst. Commun., Vol. 14. Providence, RI: American Mathematical Society, pp. 55-70.
11. G. GASPER, M. RAHMAN (1990): Basic Hypergeometric Series. Cambridge: Cambridge University Press.
12. I. M. GESSEL, C. KRATTENTHALER (1997): Cylindric partitions. Trans. Amer. Math. Soc., 349:429-479.
13. R. A. GUSTAFSON (1987): Multilateral summation theorems for ordinary and basic hypergeometric series in U(n). SIAM J. Math. Anal., 18:1576-1596.
14. R. A. GUSTAFSON (1989): The Macdonald identities for affine root systems of classical type and hypergeometric series very-well-poised on semisimple Lie algebras. In: Ramanujan International Symposium on Analysis (Pune, 1987). New Delhi: Macmillan, pp. 185-224.
15. W. J. HOLMAN, L. C. BIEDENHARN, J. D. LOUCK (1976): On hypergeometric series well-poised in SU(n). SIAM J. Math. Anal., 7:529-541.
16. Y. KAJIHARA (to appear): Euler transformation formulas for multiple basic hypergeometric series of type A and some applications. Adv. in Math.
17. P. W. KARLSSON (1971): Hypergeometric functions with integral parameter differences. J. Math. Phys., 12:270-271.
18. n basic hypergeometric series conjectured by Warnaar. Contemp. Math., 291:153-161.
19. 2k+4. Pacific J. Math., 91:419-430.
20. (1). Adv. in Math., 57: 34-70.
21. 1 sum. Ramanujan Revisited (Urbana-Champaign, IL, 1987). Boston, MA: Academic Press, pp. 473-524.
22. 2 summation theorems for U(n) basic hypergeometric series. Adv. in Math., 131:93-187.
23. 9 transformations. J. Comput. Appl. Math., 68:239-285.
24. B. MINTON (1970): Generalized hypergeometric function of unit argument. J. Math. Phys., 11:1375-1376.
25. n. J. Math. Anal. Appl.
26. H. ROSENGREN (to appear): Elliptic hypergeometric series on root systems. Adv. in Math.
27. M. SCHLOSSER (2001): Multilateral transformations of q-series with quotients of parameters that are nonnegative integral powers of q. Contemp. Math., 291:203-227.
28. 8 summation. Constr. Approx., 19:163-178.
29. M. SCHLOSSER (to appear): Elementary derivations of identities for bilateral basic hypergeometric series. Selecta Math.
30. H. S. SHUKLA (1959): A note on the sums of certain bilateral hypergeometric series. Proc. Cambridge Philos. Soc., 55:262-266.