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Further bibasic hypergeometric transformations and their applications. (English) Zbl 1107.33020

In this paper, firstly authors establish three new bibasic hypergeometric transformation formulas. They also discuss several interesting special cases of their results. Next one result obtained by U. B. Singh [J. Math. Anal. Appl. 201, No. 1, 44–56 (1996; Zbl 0851.33012)] is generalized by using Bailey’s technique. A number of new multiple series identities of the Rogers-Ramanujan type are also established with the help of this generalization.

MSC:

33D65 Bibasic functions and multiple bases
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)

Citations:

Zbl 0851.33012
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Full Text: DOI

References:

[1] Bailey, W. N., Some identities in combinatory analysis, Proc. London Math. Soc., 49, 421-435 (1947) · Zbl 0041.03403
[2] Bailey, W. N., Identities of the Rogers-Ramanujan type, Proc. London Math. Soc., 50, 1-10 (1949) · Zbl 0031.39203
[3] Chu, W. C., The Saalschütz chain reactions and multiple \(q\)-series transformations, (Ismail, M. E.H.; Koelink, T. E., Theory and Applications of Special Functions, dedicated to Mizan Rahman. Theory and Applications of Special Functions, dedicated to Mizan Rahman, Dev. Math., vol. 13 (2005), Springer), 99-122 · Zbl 1219.33018
[4] Gasper, G.; Rahman, M., Basic Hypergeometric Series (1990), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0695.33001
[5] Paule, P., On identities of the Rogers-Ramanujan type, J. Math. Anal. Appl., 107, 225-284 (1985) · Zbl 0582.10008
[6] Singh, U. B., A bibasic hypergeometric transformation associated with combinatorial identities of the Rogers-Ramanujan type, Proc. Indian Acad. Sci. Math. Sci., 105, 1, 41-51 (1995) · Zbl 0834.33013
[7] Singh, U. B., Certain bibasic hypergeometric transformation formulae and application to Rogers-Ramanujan identities, J. Math. Anal. Appl., 198, 671-684 (1996) · Zbl 0854.33017
[8] Singh, U. B., Certain bibasic hypergeometric transformations and their applications, J. Math. Anal. Appl., 201, 44-56 (1996) · Zbl 0851.33012
[9] Slater, L. J., A new proof of Rogers’ transformations of infinite series, Proc. London Math. Soc., 53, 460-475 (1951) · Zbl 0044.06102
[10] Slater, L. J., Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc., 54, 147-167 (1952) · Zbl 0046.27204
[11] Verma, A., On identities of Rogers-Ramanujan type, Indian J. Pure Appl. Math., 11, 770-790 (1980) · Zbl 0443.33005
[12] Verma, A.; Jain, V. K., Transformations between basic hypergeometric series on different bases and identities of the Rogers-Ramanujan type, J. Math. Anal. Appl., 76, 230-269 (1980) · Zbl 0443.33004
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