Related papers: Some unified integrals associated with generalized…
A short review will be made of elliptic integrals, widely applied in GPS (Global Positioning System) communications (accounting for General Relativity Theory-effects), cosmology, Black hole physics and celestial mechanics. Then a novel…
Sharp inequalitieis of Gruss type for Stieltjes integrals with application in numerical integration are provided.
We present a novel approach to the concept of gluing in mathematics by introducing the notions of a gluing data category and a gluing data functor. Our work provides a formal categorical characterization of the notion of gluing in algebraic…
Motivated by the new Laplace transforms for the Kummer's confluent hypergeometric functions $_1F_1$ obtained recently by Kim et al. [Math $\&$ Comput. Modelling, 55 (2012), pp. 1068--1071], the authors aim is to establish so far unknown…
We give a new derivation and characterisation of the generalised elliptic genus of Krichever-H\"ohn by means of a functional equation.
A general method for analytic inversion in integral geometry is proposed. All classical and some new reconstruction formulas of Radon-John type are obtained by this method. No harmonic analysis and PDE is used.
Novel analytic solutions are derived for integrals that involve the generalized Marcum Q-function, exponential functions and arbitrary powers. Simple closed-form expressions are also derived for the specific cases of the generic integrals.…
We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…
Based on Colombeau's theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic…
In this paper, authors study the generalized complete $(p,q)$-elliptic integrals of the first and the second kind as an application of generalized trigonometric functions with two parameters, and establish the Tur\'an type inequalities of…
We offer some summation formulas that appear to have great utility in probability theory. The proofs require some recent results from analysis that have thus far been applied to basic hypergeometric functions.
This paper evaluates some generalised Euler sums involving the digamma function.
An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are…
Euler's transformation formula for the Gauss hypergeometric function 2F1 is extended to hypergeometric functions of higher order. Unusually, the generalized transformation constrains the hypergeometric function parameters algebraically but…
In this paper, the authors gives a new identity for Hadamard fractional integrals. By using of this identity, the authors obtains new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for (alpha?;m)-GA-convex…
We introduce a generalization of symmetric functions and apply the resulting theory to compute the class in the Grothendieck ring of varieties of the space of geometrically irreducible hypersurfaces of a fixed degree in projective space.
In this article we study some new pointwise inequalities between rough singular integral operators, weighted maximal functions of the gradient and weighted Morrey spaces. These pointwise estimates will naturally lead us to a new class of…
We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well-known, these integrals are convergent only for a limited range of parameters. However, when one…
A generalization of the quotient integral formula is presented and some of its properties are investigated. Also the relations between two function spaces related to the spacial homogeneous spaces are derived by using general quotient…
In this paper, algorithms are developed for computing the Stirling transform and the inverse Stirling transform; specifically, we investigate a class of sequences satisfying a two-term recurrence. We derive a general identity which…