Kodai Mathematical Journal

Some inverse fractional legendre transforms of gamma function form

Alireza Ansari

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Abstract

In this paper, using the asymptotic expansion of the ratio of gamma functions, we obtain new inversion formulas for the fractional Legendre transforms. These formulas are given in terms of some integral representations of the inverse Mellin transforms. Also, the closed forms of solutions of the fractional Laplace and Helmholtz equations are obtained by these inversion formulas.

Article information

Source
Kodai Math. J., Volume 38, Number 3 (2015), 658-671.

Dates
First available in Project Euclid: 30 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1446210600

Digital Object Identifier
doi:10.2996/kmj/1446210600

Mathematical Reviews number (MathSciNet)
MR3417527

Zentralblatt MATH identifier
1333.26004

Citation

Ansari, Alireza. Some inverse fractional legendre transforms of gamma function form. Kodai Math. J. 38 (2015), no. 3, 658--671. doi:10.2996/kmj/1446210600. https://projecteuclid.org/euclid.kmj/1446210600


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