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Proceedings of the American Mathematical Society

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An integral generalization
of the $q$-binomial theorem and an application


Author: Yunkang Liu
Journal: Proc. Amer. Math. Soc. 124 (1996), 165-168
MSC (1991): Primary 33D99; Secondary 45J05
DOI: https://doi.org/10.1090/S0002-9939-96-03235-2
MathSciNet review: 1307548
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Abstract | References | Similar Articles | Additional Information

Abstract: An integral identity which generalizes the $q$-binomial theorem is presented. This identity is used to determine the exponential expansion of the solution of an integro-differential equation.


References [Enhancements On Off] (What's this?)

  • 1 G. Gasper and M. Rahman, Basic hypergeometric series, Cambridge Univ. Press, Cambridge, 1990.MR 91d:33034
  • 2 A. Iserles, On the generalized pantograph functional-differential equation, European J. Appl. Math. 4 (1993), 1--38.MR 94f:34127
  • 3 A. Iserles and Y. Liu, On pantograph integro-differential equations, J. Integral Equations Appl. 6 (1994), 213--237.MR 95g:45008

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Additional Information

Yunkang Liu
Affiliation: Department of Applied Mathematics and Theoretical Physics University of Cambridge Silver Street Cambridge, CB3 9EW England
Email: yl@amtp.cam.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-96-03235-2
Received by editor(s): July 25, 1994
Communicated by: Hal L. Smith
Article copyright: © Copyright 1996 American Mathematical Society

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