Further Generalization of Kobayashi's Gamma Function

In this paper, we introduce a further generalization of the gamma function involving Gauss hypergeometric function 2F1 (a, b; c; z

On Generalized Hurwitz-Lerch Zeta Distributions

In this paper, we introduce a function which is an extension to the general Hurwitz-Lerch Zeta function. Having defined the incomplete generalized beta type-2 and incomplete generalized gamma functions, some differentiation formulae are established for these incomplete functions. We have introduced two new statistical distributions, termed as generalized Hurwitz-Lerch Zeta beta type-2 distribution and generalized Hurwitz-Lerch Zeta gamma distribution and then derived the expressions for the moments, distribution function, the survivor function, the hazard rate function and the mean residue life function for these distributions. Graphs for both these distributions are given, which reflect the role of shape and scale parameters

Certain Expansion Formulae Involving a Basic Analogue of Fox’s H-Function

Certain expansion formulae for a basic analogue of the Fox’s H-function have been derived by the applications of the q-Leibniz rule for the Weyl type q-derivatives of a product of two functions. Expansion formulae involving a basic analogue of Meijer’s G-function and MacRobert’s E-function have been derived as special cases of the main results

Wavelet Transform of Fractional Integrals for Integrable Boehmians

The present paper deals with the wavelet transform of fractional integral operator (the Riemann- Liouville operators) on Boehmian spaces. By virtue of the existing relation between the wavelet transform and the Fourier transform, we obtained integrable Boehmians defined on the Boehmian space for the wavelet transform of fractional integrals

On hypergeometric generalized negative binomial distribution

It is shown that the hypergeometric generalized negative binomial distribution has moments of all positive orders, is overdispersed, skewed to the right, and leptokurtic. Also, a three-term recurrence relation for computing probabilities from the considered distribution is given. Application of the distribution to entomological field data is given and its goodness-of-fit is demonstrated

On the numerical evaluation of algebro-geometric solutions to integrable equations

Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis not related to automorphisms of the curve, we study symplectic transformations to an adapted basis and give explicit formulae for M-curves. As examples we discuss solutions of the Davey-Stewartson and the multi-component nonlinear Schr\"odinger equations.Comment: 29 pages, 20 figure

On mikusinski's operators of fractional integration

In the field F of convolution quotients,  b∝ is the operator of integration of fractional order ∝ and b∝ f   Is the Riemann - Liouville integral of order   ∝ of f. In this paper we give a generalization of this operator, which is denoted as b∝,va . Some particular cases are mentioned and the inverse operator is obtained

Probability density functions involving a generalized r–Gauss hypergeometric function

The aim of this paper is to study r–generalized gamma functions of a particular form.Moreover, we define a new probability density function (p.d.f) involving these new generalized functions. Some basic functions associated with the p.d.f’s, such as moment generating functions, mean residue functions and hazard rate functions are derived

A generalized beta function and associated probability density

We introduce and establish some properties of a generalized form of the beta function. Corresponding generalized incomplete beta functions are also defined. Moreover, we define a new probability density function (pdf) involving this new generalized beta function. Some basic functions associated with the pdf, such as moment generating function, mean residue function, and hazard rate function are derived. Some special cases are mentioned. Some figures for pdf, hazard rate function, and mean residue life function are given. These figures reflect the role of shape and scale parameters

The inversion, formulae for some bessel and hypergeometric transforms

By an appeal to the Laplace transform and their inverses we have obtained five inversión formulae for some Bessel function transforms. The inversion formula for hyperqeometric transforms have been given whose kernel are the confluent hypergeometric function  1F1(γ - a;  γ; μx) and Gauss hypergeometric function  2F1( a, β, γ;  - 1/ μ x). The results given earlier by Gómez López [8] follow as special cases of our results given in section. 3