Multiple elliptic integrals related to the generalized Clebsch–Gordan (CG) integral are of importance in many areas physics and special functions theory. Zhou has introduced applied Legendre function-based techniques prove symbolic evaluations for CG form involving twofold threefold products complete expressions, this includes Zhou's remarkable proof an open problem due Wan. The foregoing consi...

We consider integrals of type ∫ On u1 11 . . . u an 1nu b1 21 . . . u bn 2n du, with respect to the Haar measure on the orthogonal group. We establish several remarkable invariance properties satisfied by such integrals, by using combinatorial methods. We present as well a general formula for such integrals, as a sum of products of factorials. Introduction The computation of polynomial integral...

Explicit formulae for Weber-Schafheitlin’s type integrals with exponent 1 are derived. The results of these integrals are distributions on R+.

The Weyl criterion is shown in the terms of Price functions and Haar type functions. We define the so-called modified integrals of Price and Haar type functions and obtain the analogues of the criterion of Weyl, the inequalities of LeVeque and Erdös-Turan and the formula of Koksma in the terms of the modified integrals of Price and Haar type functions.

Minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. Also related inequalities to Minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. Several examples are given to illustrate the validity of theorems. Some results on Chebyshev and Minkowski type inequalities are obtained.

Let Ñt be a standard compensated Poisson process on [0, 1]. We prove a new characterization of anticipating integrals of the Skorohod type with respect to Ñ , and use it to obtain several counterparts to well established properties of semimartingale stochastic integrals. In particular we show that, if the integrand is sufficiently regular, anticipating Skorohod integral processes with respect t...

This review presents techniques for the computation of multi-electron integrals over Cartesian and solid-harmonic Gaussian-type orbitals as used in standard electronic-structure investigations. The review goes through the basics for oneand two-electron integrals, discuss details of various two-electron integral evaluation schemes, approximative methods, techniques to compute multi-electron inte...

Using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of Hammerstein type . The mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). The procedure of this method is so fast and don't need high cpu and complicated programming. The advantages of this method are that we can applied for those integral equations whi...