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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Summation, transformation, and expansion formulas for bibasic series


Author: George Gasper
Journal: Trans. Amer. Math. Soc. 312 (1989), 257-277
MSC: Primary 33A70; Secondary 33A35
MathSciNet review: 953537
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0953537-0
PII: S 0002-9947(1989)0953537-0
Keywords: Basic hypergeometric series, bibasic expansion formulas, Euler's transformation formula, Lagrange inversion, summation and transformation formulas
Article copyright: © Copyright 1989 American Mathematical Society