Inequalities involving Bessel functions of the first kind.
Inequalities involving generalized Bessel functions.
Information Matrix for Beta Distributions
2000 Mathematics Subject Classification: 33C90, 62E99.The Fisher information matrix for three generalized beta distributions are derived.
Integrability Theorems For Jacobi Series
Integral and computational representation of summation which extends a Ramanujan's sum
Integral averages of multiple Poisson kernels.
Integral representation of a solution of Heun's general equation.
Integral representation of orthogonal exponential polynomials
Integral representation of the -th derivative in de Branges-Rovnyak spaces and the norm convergence of its reproducing kernel
In this paper, we give an integral representation for the boundary values of derivatives of functions of the de Branges–Rovnyak spaces , where is in the unit ball of . In particular, we generalize a result of Ahern–Clark obtained for functions of the model spaces , where is an inner function. Using hypergeometric series, we obtain a nontrivial formula of combinatorics for sums of binomial coefficients. Then we apply this formula to show the norm convergence of reproducing kernel of evaluation...
Integral representation of the solutions to Heun's biconfluent equation.
Integral representations and binomial coefficients.
Integral representations for multiple Hermite and multiple Laguerre polynomials
We give integral representations for multiple Hermite and multiple Laguerre polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.
Integral Representations of Functional Series with Members Containing Jacobi Polynomials
MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10In this article we establish a double definite integral representation, and two other indefinite integral expressions for a functional series and its derivative with members containing Jacobi polynomials.
Integral representations of generalized Lauricella hypergeometric functions.
Integral Representations of Generalized Mathieu Series Via Mittag-Leffler Type Functions
Mathematics Subject Classification: 33C05, 33C10, 33C20, 33C60, 33E12, 33E20, 40A30The main purpose of this paper is to present a number of potentially useful integral representations for the generalized Mathieu series as well as for its alternating versions via Mittag-Leffler type functions.
Integrali di funzioni di Anger, Weber ed Airy-Hardy
Integrality of two variable Kostka functions.
Integrals and polygamma representations for binomial sums.
Integrals involving Gegenbauer and Hermite polynomials on the imaginary axis.
Integrals involving Hermite polynomials, generalized hypergeometric series and Fox's H-function, and Fourier-Hermite series for products of generalized hypergeometric functions
We evaluate an integral involving an Hermite polynomial, a generalized hypergeometric series and Fox's H-function, and employ it to evaluate a double integral involving Hermite polynomials, generalized hypergeometric series and the H-function. We further utilize the integral to establish a Fourier-Hermite expansion and a double Fourier-Hermite expansion for products of generalized hypergeometric functions.