Summation, transformation, and expansion formulas for bibasic series

Gasper, George

doi:10.1090/S0002-9947-1989-0953537-0

Summation, transformation, and expansion formulas for bibasic series
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Trans. Amer. Math. Soc. 312 (1989), 257-277 Request permission

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 $q$-Lagrange inversion formula, and some quadratic, cubic and quartic summation formulas.

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series

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