625 research outputs found
On q-Laplace Transforms of the q-Bessel Functions
Mathematics Subject Classification: 33D15, 44A10, 44A20The present paper deals with the evaluation of the q-Laplace transforms
of a product of basic analogues of the Bessel functions. As applications,
several useful special cases have been deduced
On Generalized Weyl Fractional q-Integral Operator Involving Generalized Basic Hypergeometric Functions
Mathematics Subject Classification: 33D60, 33D90, 26A33Fractional q-integral operators of generalized Weyl type, involving generalized basic hypergeometric functions and a basic analogue of Fox’s H-function have been investigated. A number of integrals involving various q-functions have been evaluated as applications of the main results
On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function
2000 Mathematics Subject Classification: 33D60, 26A33, 33C60The present paper envisages the applications of Riemann-Liouville fractional q-integral operator to a basic analogue of Fox H-function. Results involving the basic hypergeometric functions like Gq(.), Jv(x; q), Yv(x; q),Kv(x; q), Hv(x; q) and various other q-elementary functions associated with the Riemann-Liouville fractional q-integral operator have been deduced as special cases of the main result
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
Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics
Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.The object of this article is to present the computational solution of one-dimensional space-time fractional Schrödinger equation occurring in quantum mechanics. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the H-function. It provides an elegant extension of a result given earlier by Debnath, and by Saxena et al. The main result is obtained in the form of Theorem 1. Three special cases of this theorem are given as corollaries. Computational representation of the fundamental solution of the proposed equation is also investigated
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 a Class of Generalized Elliptic-type Integrals
The aim of this paper is to study a generalized form of elliptic-type integrals
which unify and extend various families of elliptic-type integrals studied
recently by several authors. In a recent communication [1] we
have obtained recurrence relations and asymptotic formula for this generalized
elliptic-type integral. Here we shall obtain some more results which
are single and multiple integral formulae, differentiation formula, fractional
integral and approximations for this class of generalized elliptic-type integrals
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
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