Open Access
October 2015 Some inverse fractional legendre transforms of gamma function form
Alireza Ansari
Kodai Math. J. 38(3): 658-671 (October 2015). DOI: 10.2996/kmj/1446210600


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.


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Alireza Ansari. "Some inverse fractional legendre transforms of gamma function form." Kodai Math. J. 38 (3) 658 - 671, October 2015.


Published: October 2015
First available in Project Euclid: 30 October 2015

zbMATH: 1333.26004
MathSciNet: MR3417527
Digital Object Identifier: 10.2996/kmj/1446210600

Rights: Copyright © 2015 Tokyo Institute of Technology, Department of Mathematics

Vol.38 • No. 3 • October 2015
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