The Dirac Equation is solved approximately for relativistic generalized Woods-Saxon potential including Coulomb-like tensor in exact pseudospin and spin symmetry limits. bound states energy eigenvalues are found by using wavefunction boundary conditions, corresponding radial wavefunctions obtained terms of hypergeometric function. Some numerical examples given the dependence on quantum numbers ...

The starting point of this paper are the Mittag–Leffler polynomials investigated in details by H. Bateman in [1]. Based on generalized integer powers of real numbers and deformed exponential function, we introduce deformed Mittag–Leffler polynomials defined by appropriate generating function. We investigate their recurrence relations, hypergeometric representation and orthogonality. Since they ...

This paper presents a new connection between the generalized Marcum-Q function and the confluent hypergeometric function of two variables, Φ3. This result is then applied to the closed-form characterization of the bivariate Nakagami-m distribution and of the distribution of the minimum eigenvalue of correlated non-central Wishart matrices, both important in communication theory. New expressions...

In this paper, we propose the another yet generalization of Stirling numbers of the rst kind for non-integer values of their arguments. We discuss the analytic representations of Stirling numbers through harmonic numbers, the generalized hypergeometric function and the logarithmic beta integral. We present then in nite series involving Stirling numbers and demonstrate how they are related to Eu...

The objective of this paper is to define and study further generalization of extended gamma, extended beta and extended hypergeometric functions. Closed form representation of the generalized extended gamma function is derived in the form of Meijer’s G-function. Some of their properties and special cases are also derived. These functions have applications in probability theory, reliability, ast...

tions F(3), F(4), Lauricella’s quadruple hypergeometric function F A , Exton’s multiple hypergeometric functions X E:G;H , K10, K13, X8, (k)H 2 , (k)H 4 , Erdélyi’s multiple hypergeometric function Hn,k, Khan and Pathan’s triple hypergeometric function H (P) 4 , Kampé de Fériet’s double hypergeometric function F E:G;H , Appell’s double hypergeometric function of the second kind F2, and the Sriv...

In this paper, using the modified beta function involving generalized M-series in its kernel, we described new extensions for Lauricella hypergeometric functions $F_{A}^{(r)}$, $F_{B}^{(r)}$, $F_{C}^{(r)}$ and $F_{D}^{(r)}$. Furthermore, obtained various integral representations newly defined extended functions. Then, solution of fractional differential equations functions, as examples.