SOME INVERSE FRACTIONAL LEGENDRE TRANSFORMS OF GAMMA FUNCTION FORM

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.