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

DOI:
https://doi.org/10.1090/S0025-5718-1974-0371019-7

MathSciNet review:
0371019

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Abstract | References | Similar Articles | Additional Information

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.

**[1]**M. Abramowitz & I. A. Stegun (Editors),*Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables*, Nat. Bur. Standards Appl. Math. Series, 55, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR**29**# 4914. MR**0167642 (29:4914)****[2]**A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi,*Higher Transcendental Functions*. Vols. 1, 2, McGraw-Hill, New York, 1953. MR**15**, 419.**[3]**A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi,*Tables of Integral Transforms*. Vol. 1, McGraw-Hill, New York, 1954. MR**15**, 868.**[4]**Bernard J. Laurenzi, "Derivatives of Whittaker functions and with respect to order*k*,"*Math. Comp.*, v. 27, 1973, pp. 129-132. MR**0364694 (51:948)****[5]**L. J. Slater,*Confluent Hypergeometric Functions*, Cambridge Univ. Press, New York, 1960. MR**21**#5753. MR**0107026 (21:5753)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0371019-7

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