Related papers: New integral representations for the Fox-Wright fu…
In this paper our aim is to present the completely monotonicity and convexity properties for the Wright function. As consequences of these results, we present some functional inequalities. Moreover, we derive the monotonicity and…
A new variant of the exact Fradkin representation of the Green's function $G_c(x,y|gU)$, defined for arbitrary external potential $U$, is presented. Although this new approach is very similar in spirit to that previously derived by Fried…
The computation and inversion of the noncentral beta distribution $B_{p,q}(x,y)$ (or the noncentral $F$-distribution, a particular case of $B_{p,q}(x,y)$) play an important role in different applications. In this paper we study the…
In this present investigation, we found a set of sufficient conditions to be imposed on the parameters of the Fox H-functions which allow us to conclude that it is non-negative. As applications, various new facts regarding the Fox-Wright…
In this paper, the incomplete Pochhammer ratios are defined in terms of the incomplete beta function $B_{y}(x,z)$. With the help of these incomplete Pochhammer ratios, we introduce new incomplete Gauss, confluent hypergeometric and Appell's…
The aim of this article is to give a generalization of the Cauchy-Pompeiu integral formula for functions valued in parameter-depending elliptic algebras with structure polynomial $X^2 + \beta X + \alpha$ where $\alpha$ and $\beta$ are real…
We build on a recent paper on Fourier expansions for the Riemann zeta function. We establish Fourier expansions for certain $L$-functions, and offer series representations involving the Whittaker function $W_{\gamma,\mu}(z)$ for the…
Our purpose in this present paper is to investigate generalized integration formulas containing the generalized $k$-Bessel function $W_{v,c}^{k}(z)$ to obtain the results in representation of Wright-type function. Also, we establish certain…
In this survey we discuss derivatives of the Wright functions (of the first and the second kind) with respect to parameters. Differentiation of these functions leads to infinite power series with coefficient being quotients of the digamma…
The main purpose of this paper is to provide a novel approach to deriving formulas for the p-adic q-integral including the Volkenborn integral and the p-adic fermionic integral. By applying integral equations and these integral formulas to…
In the paper, the authors establish integral representations of some functions related to the remainder of Burnside's formula for the gamma function and find the (logarithmically) complete monotonicity of these and related functions. These…
Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and…
It is defined $\Gamma_{p,q}$ function, a generalize of $\Gamma$ function. Also, we defined $\psi_{p,q}$-analogue of the psi function as the log derivative of $\Gamma_{p,q}$. For the $\Gamma_{p,q}$ -function, are given some properties…
We use generating functions to express orthogonality relations in the form of $q$-beta integrals. The integrand of such a $q$-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal
Our aim in this paper, is to establish certain new integrals for the the (p,q)-Mathieu--power series. In particular, we investigate the Mellin-Barnes type integral representations for a particular case of thus special function. Moreover, we…
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…
We consider the asymptotic expansion of the Wright function \[W_{\lambda,\mu}(z)=\sum_{n=0}^\infty\frac{z^n}{n! \Gamma(\lambda n+\mu)}\qquad (\lambda>-1)\] for large (positive and negative) variable and large parameter $\mu$. The analysis…
This paper is mostly a survey, with a few new results. The first part deals with functional equations for q-exponentials, q-binomials and q-logarithms in q-commuting variables and more generally under q-Heisenberg relations. The second part…
In this paper, the authors study the matrix-valued harmonic functions and characterize them by the Poisson integral of functions in non-commutative BMO (bounded mean oscillation) spaces. This provides a very satisfactory non-commutative…
In the present paper we use the expansion formula of the polylogarithm function to construct approximations of the Caputo derivative which are related to the midpoint approximation of the integral in the definition of the Caputo derivative.…