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An Indefinite Bibasic Summation Formula and Some Quadratic, Cubic and Quartic Summation and Transformation Formulas

Published online by Cambridge University Press:  20 November 2018

George Gasper  and
Mizan Rahman
George Gasper
Affiliation:
Northwestern University, Evanston, Illinois
Mizan Rahman
Affiliation:
Carleton University, Ottawa, Ontario
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Let denote the q-shifted factorial, and set Recently, Gasper [7] showed that some bibasic summation formulas derived by Carlitz [5], Al-Salam and Verma [1], and Wm. Gosper could be extended to the indefinite bibasic summation formula where p and q are independent bases and a, b, c are arbitrary parameters.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 1 , 01 February 1990 , pp. 1 - 27
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Al-Salam, W.A. and Verma, A., On quadratic transformations of basic series, SIAM J. Math. Anal. 75 (1984), 414-20.Google Scholar
2. Askey, R., The q-gamma and the q-beta functions, Applicable Analysis 8 (1978), 125–141.Google Scholar
3. Bailey, W.N., Generalized hypergeometric series, (Cambridge University Press, London, 1935) (reprinted by Stechert-Hafner, New York, 1964).Google Scholar
4. Bailey, W.N., Well-poised basic hypergeometric series, Quart. J. Math. (Oxford) 18 (1947), 157–166.Google Scholar
5. Carlitz, L., Some inverse relations, Duke Math. J. 40(1973), 893–901.Google Scholar
6. Fields, J.L. and Wimp, J., Expansions of hypergeometric functions in hypergeometric functions, Math. Comp. 75 (1961), 390–395.Google Scholar
7. Gasper, G., Summation, transformation, and expansion formulas for the bibasic series, Trans. Amer. Math. Soc, 372 (1989), 257- 277.Google Scholar
8. Gasper, G. and Rahman, M., Basic hypergeometric series, Cambridge University Press, to appear.Google Scholar
9. Gessel, I. and Stanton, D., Strange evaluations of hypergeometric series, SIAM J. Math. Anal. 13 (1982), 295–308.Google Scholar
10. Rahman, M., Some quadratic and cubic summation formulas for basic hypergeometric series, to appear.Google Scholar
11. Sears, D.B., Transformations of basic hypergeometric functions of special type, Proc. London Math. Soc. (2) 52 (1951), 467–483.Google Scholar
12. Slater, L.J., Generalized hyper geometric functions, (Cambridge University Press, London, 1966).Google Scholar
13. Verma, A., Some transformations of series with arbitrary terms, Institute Lombardo (Rend. Sc.) A. 106 (1972), 342–353.Google Scholar