Abstract The scope of our investigation is to study the geometric properties normalized form combination generalized Lommel–Wright function $J_{\nu ,\lambda }^{\mu ,m}$ J ? , ? ? m </mm...

The object of this paper is to establish an general Eulerian integral involving the product of two multivariable I-functions defined by Nambisan et al [2], a class of multivariable polynomials and a generalized hypergeometric function which provide unification and extension of numerous results. We will study the particular cases concerning the multivariable H-function and the Srivastava-Daoust ...

We give an example of solutions the connection problem associated with a certain system linear $q$-difference equations recently introduced by Park. The result contains formulas $q$-Lauricella hypergeometric function $\varphi_{D}$ and those $q$-generalized ${}_{N+1}\varphi_{N}$ as special cases.

Herein, we calculate reduction formulas for some generalized hypergeometric functions m+1Fmz in terms of elementary as well incomplete beta functions. For this purpose, the n-th order derivative function zγBzα,β with respect to z. As corollaries, obtain these argument unity functions,

In the present paper, the author applies some of his earlier results which extend the well-known Hille-Hardy formula for the Laguerre polynomials to certain classes of generalized hypergeometric polynomials in order to derive various generalizations of a bilinear generating function for the Jacobi polynomials proved recently by Carlitz. The corresponding results for the polynomials of Legendre,...

The main object of this paper is to investigate the solution of the following free electron laser equations associated with generalized MittagLeffler function and a confluent hypergeometric function in two variables: Dα τ h(τ) = ω ∫ τ 0 t β−1 h(τ − t)E σ,β(iνt σ)dt+ δf(τ), where γ, δ, ω ∈ C; ν ∈ R,α > 0, σ > 0, β > 0; E σ,β(z) is the generalized Mittag-Leffler function and Dα τ h(τ) = λ Γ(γ) ∫ ...

Introduction/purpose: Certain integrals involving the generalized Mittag-Leffler function with different types of polynomials are established. Methods: The properties used in conjunction kinds such as Jacobi, Legendre, and Hermite order to evaluate their integrals. Results: Some integral formulae Legendre function, Bessel Maitland hypergeometric functions derived. Conclusions: results obtained ...

where θ = n̄Γ(k)Γ(k+1/μ) and H(·) is the Fox generalized hypergeometric function or H-function. For μ = 1 the NBD is recovered. For μ > 1 Pn is not infinitely divisible and the factorial cumulants of the distribution exhibit nontrivial sign-changing oscillations. Eqs. (2)-(3) involve as special and limiting cases the Poisson transform of numerous classical probability densities such as the Chi, ...