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Mathematics of Computation

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Finite sum representations for partial derivatives of special functions with respect to parameters

Author: R. G. Buschman
Journal: Math. Comp. 28 (1974), 817-824
MSC: Primary 65D20; Secondary 33A30
MathSciNet review: 0371019
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Abstract: The Mellin transformation is used as a method for discovery of cases where the partial derivatives with respect to parameters for certain Whittaker and Bessel functions can be expressed in terms of finite sums involving these functions. These results are easily generalized to the G-function, from which, by specialization, formulas involving hypergeometric and other functions can be obtained.

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Keywords: Whittaker functions, Bessel functions, hypergeometric functions, Gegenbauer functions, Legendre functions, G-functions, derivative with respect to order, Mellin transformations
Article copyright: © Copyright 1974 American Mathematical Society

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