Note on an integral by Fritz Oberhettinger

Robert Reynolds; Allan Stauffer; Robert Reynolds; Allan Stauffer

doi:10.3934/math.2021034

AIMS Mathematics

2021, Volume 6, Issue 1: 564-568. doi: 10.3934/math.2021034

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Research article

Note on an integral by Fritz Oberhettinger

Robert Reynolds ^,,
Allan Stauffer

Department of Mathematics, York University, 4700 Keele Street, Toronto, M3J1P3, Canada

Received: 08 October 2020 Accepted: 19 October 2020 Published: 21 October 2020
MSC : 01A55, 11M06, 11M35, 30-02, 30D10, 30D30, 30E20

In 1974 Fritz Oberhettinger published the Tables of Mellin Transforms. We derive the correct result for one of these integrals along with some interesting special cases.
- entries of Oberhettinger,
- hyperbolic integrals,
- Hurwitz zeta function
Citation: Robert Reynolds, Allan Stauffer. Note on an integral by Fritz Oberhettinger[J]. AIMS Mathematics, 2021, 6(1): 564-568. doi: 10.3934/math.2021034

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Abstract

In 1974 Fritz Oberhettinger published the Tables of Mellin Transforms. We derive the correct result for one of these integrals along with some interesting special cases.

References

[1]	F. Oberhettinger, Tables of Mellin Transforms, 1st ed., Springer-Verlag, Berlin Heidelberg, 1974.
[2]	M. Abramowitz, I. A. Stegun, (Eds) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing, New York, Dover, 1982.
[3]	A. Erdéyli, W. Magnus, F. Oberhettinger, F. G. Tricomi, Higher Transcendental Functions, Vol. 1, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953.
[4]	A. Erdéyli, W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms, Vol. I, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954.
[5]	I. S. Gradshteyn, I. M. Ryzhik, Tables of Integrals, Series and Products, 6 Ed, Academic Press, USA, 2000.
[6]	R. Reynolds, A. Stauffer, A Method for Evaluating Definite Integrals in Terms of Special Functions with Examples. International Mathematical Forum, 15 (2020), 235-244. doi: 10.12988/imf.2020.91272

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