Summation, transformation, and expansion formulas for bibasic series

Author:

Gasper George

Abstract

An indefinite bibasic sum containing three parameters is evaluated and used to derive bibasic extensions of Euler’s transformation formula and of a Fields and Wimp expansion formula. It is also used to derive a transformation formula involving four independent bases, a q q -Lagrange inversion formula, and some quadratic, cubic and quartic summation formulas.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference25 articles.

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2. Generalized basic hypergeometric series with unconnected bases. II;Agarwal, R. P.;Quart. J. Math. Oxford Ser. (2),1967

3. On quadratic transformations of basic series;Al-Salam, W. A.;SIAM J. Math. Anal.,1984

4. On basic hypergeometric series, mock theta functions, and partitions. I;Andrews, G. E.;Quart. J. Math. Oxford Ser. (2),1966

5. Inequalities for polynomials;Askey, Richard,1986

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