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

Author(s): Yunkang Liu
Journal: Proc. Amer. Math. Soc. 124 (1996), 165-168.
MSC (1991): Primary 33D99; Secondary 45J05
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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:

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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