Inequalities involving a logarithmically convex function and their applications to special functions.
Inequalities involving Bessel functions of the first kind.
Inequalities involving generalized Bessel functions.
Inequalities on the Lambert function and hyperpower function.
Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes
We first characterize the increasing eigenfunctions associated to the following family of integro-differential operators, for any α, x>0, γ≥0 and fa smooth function on , where the coefficients ,σ≥0 and the measure ν, which satisfies the integrability condition ∫0∞(1∧r2)ν(dr)<+∞, are uniquely determined by the distribution of a spectrally negative, infinitely divisible random variable, with characteristic exponent ψ. L(γ) is known to be the infinitesimal generator of a positive...
Infinite families of accelerated series for some classical constants by the Markov-WZ Method.
Infinite sums as linear combinations of polygamma functions
Information Matrix for Beta Distributions
2000 Mathematics Subject Classification: 33C90, 62E99.The Fisher information matrix for three generalized beta distributions are derived.
Integer powers of arcsin.
Integrability Theorems For Jacobi Series
Integral and computational representation of summation which extends a Ramanujan's sum
Integral averages of multiple Poisson kernels.
Integral identities and constructions of approximations to zeta-values
Some general construction of linear forms with rational coefficients in values of Riemann zeta-function at integer points is presented. These linear forms are expressed in terms of complex integrals of Barnes type that allows to estimate them. Some identity connecting these integrals and multiple integrals on the real unit cube is proved.
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.