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...

Epstein-Hubbell 1963 elliptic-type integrals occur in radiation field problems. In this paper, we consider a generalization of the elliptic-type integrals introduced by Kalla and Tuan 1996 and developed by Salman 2006. We give some recurrence relations for this generalized special function. Some of these relations can be used for analytic continuation to different domains. Asymptotic relations ...

We give an identity which is conjectured and proved by using an implementation [3] in multi-WZ [5]. 0. Introduction There are relatively few known non-trivial evaluations of n-dimensional integrals, with arbitrary n. Celebrated examples are the Selberg and the Metha-Dyson integrals, as well as the Macdonald constant term ex-conjectures for the various infinite families of root systems. They are...

We prove new upper and lower bounds for Banach space-valued stochastic integrals with respect to a compensated Poisson random measure. Our estimates apply to Banach spaces with non-trivial martingale (co)type and extend various results in the literature. We also develop a Malliavin framework to interpret Poisson stochastic integrals as vector-valued Skorohod integrals, and prove a Clark-Ocone r...

We derive Edgeworth-type expansions for Skorohod and Itô integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain Stein approximation bounds for stochastic integrals, which apply to SDE solutions and to multiple stochastic integrals.

The arithmetic geometric mean algorithm for calculation of elliptic integrals of the first type was introduced by Gauss. The analog algorithm for Abelian integrals of genus 2 was introduced by Richelot (1837) and Humbert (1901). We present the analogous algorithm for Abelian integrals of genus 3.

We propose a geometric interpretation of the classical Rankin-Selberg method for GL(n) in the framework of the geometric Langlands program. Our main result is local, its classical counterpart is the RankinSelberg computation of convolution of two Hecke eigenforms with an Eisenstein series. For n = 2 we apply it to prove a global result that gives a geometric version of the computation of the sc...