The Weyl Integration Formula

2004 ◽  
pp. 112-116
Author(s):  
Daniel Bump
Keyword(s):  
Integration Formula

A note on fractional integral operator associated with multiindex Mittag-Leffler functions

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1931-1939 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Fractional Integral ◽  
Fractional Integration ◽  
Fractional Integral Operator ◽  
Integration Formula ◽  
Special Cases

Recently Kiryakova and several other ones have investigated so-called multiindex Mittag-Leffler functions associated with fractional calculus. Here, in this paper, we aim at establishing a new fractional integration formula (of pathway type) involving the generalized multiindex Mittag-Leffler function E?,k[(?j,?j)m;z]. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

scholarly journals Unconditional Positive Stable Numerical Solution of Partial Integrodifferential Option Pricing Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
M. Fakharany ◽  
R. Company ◽  
L. Jódar
Keyword(s):  
Option Pricing ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Stable Process ◽  
Integration Formula ◽  
Pricing Models ◽  
Integral Term ◽  
Pricing Problems ◽  
Stability And Consistency ◽  
Partial Integrodifferential Equation

This paper is concerned with the numerical solution of partial integrodifferential equation for option pricing models under a tempered stable process known as CGMY model. A double discretization finite difference scheme is used for the treatment of the unbounded nonlocal integral term. We also introduce in the scheme the Patankar-trick to guarantee unconditional nonnegative numerical solutions. Integration formula of open type is used in order to improve the accuracy of the approximation of the integral part. Stability and consistency are also studied. Illustrative examples are included.

scholarly journals Meet Andréief, Bordeaux 1886, and Andreev, Kharkov 1882–1883

2019 ◽  
Vol 08 (02) ◽  
pp. 1930001 ◽  
Author(s):  
Peter J. Forrester
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Integration Formula ◽  
Historical Information ◽  
Sciences Physiques

The paper “Note sur une relation entre les intégrales définies des produits des fonctions” by C. Andréief is an often cited paper in random matrix theory, due to it containing what is now referred to as Andréief’s integration formula. Nearly all citing works state the publication year as 1883. However, the journal containing the paper, Mémories de la Societé des Sciences physiques et naturelles de Bordeaux, issue 3 volume 2 actually appeared in 1886. In addition to clarifying this point, some historical information relating to C. Andréief (better known as K. A. Andreev) and the lead up to this work is given, as is a review of some of the context of Andréief’s integration formula.

scholarly journals On Functional Hamilton–Jacobi and Schrödinger Equations and Functional Renormalization Group

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1657
Author(s):  
Mikhail G. Ivanov ◽  
Alexey E. Kalugin ◽  
Anna A. Ogarkova ◽  
Stanislav L. Ogarkov
Keyword(s):  
Renormalization Group ◽  
Schrödinger Equation ◽  
Functional Equations ◽  
Schrodinger Equation ◽  
Constant Field ◽  
Integration Formula ◽  
Invariant Solutions ◽  
Rigorous Derivation ◽  
Translation Invariant ◽  
Functional Renormalization Group

We consider the functional Hamilton–Jacobi (HJ) equation, which is the central equation of the holographic renormalization group (HRG), functional Schrödinger equation, and generalized Wilson–Polchinski (WP) equation, which is the central equation of the functional renormalization group (FRG). These equations are formulated in D-dimensional coordinate and abstract (formal) spaces. Instead of extra coordinates or an FRG scale, a “holographic” scalar field Λ is introduced. The extra coordinate (or scale) is obtained as the amplitude of delta-field or constant-field configurations of Λ. For all the functional equations above a rigorous derivation of corresponding integro-differential equation hierarchies for Green functions (GFs) as well as the integration formula for functionals are given. An advantage of the HJ hierarchy compared to Schrödinger or WP hierarchies is that the HJ hierarchy splits into independent equations. Using the integration formula, the functional (arbitrary configuration of Λ) solution for the translation-invariant two-particle GF is obtained. For the delta-field and the constant-field configurations of Λ, this solution is studied in detail. A separable solution for a two-particle GF is briefly discussed. Then, rigorous derivation of the quantum HJ and the continuity functional equations from the functional Schrödinger equation as well as the semiclassical approximation are given. An iterative procedure for solving the functional Schrödinger equation is suggested. Translation-invariant solutions for various GFs (both hierarchies) on delta-field configuration of Λ are obtained. In context of the continuity equation and open quantum field systems, an optical potential is briefly discussed. The mode coarse-graining growth functional for the WP action (WP functional) is analyzed. Based on this analysis, an approximation scheme is proposed for the generalized WP equation. With an optimized (Litim) regulator translation-invariant solutions for two-particle and four-particle amputated GFs from approximated WP hierarchy are found analytically. For Λ=0 these solutions are monotonic in each of the momentum variables.

The Duistermaat–Heckman integration formula on flag manifolds

1990 ◽  
Vol 31 (3) ◽  
pp. 616-638 ◽  
Author(s):  
R. F. Picken
Keyword(s):  
Flag Manifolds ◽  
Integration Formula

A fourth degree integration formula for the n-dimensional simplex

2009 ◽  
Vol 59 (12) ◽  
pp. 2990-2993 ◽  
Author(s):  
Wei Dan ◽  
Ren-hong Wang
Keyword(s):  
Integration Formula ◽  
Dimensional Simplex ◽  
Fourth Degree

scholarly journals The generalized method of exhaustion

2002 ◽  
Vol 31 (6) ◽  
pp. 345-351 ◽  
Author(s):  
Anthony A. Ruffa
Keyword(s):  
Velocity Distribution ◽  
Group Velocity ◽  
Geometric Approach ◽  
Integration Formula ◽  
Usual Procedure ◽  
Integrable Functions ◽  
Algebraic Generalization ◽  
Riemann Integrable Functions ◽  
Simple Integration

The method of exhaustion is generalized to a simple integration formula that is valid for the Riemann integrable functions. Both a geometric approach (following the usual procedure for the method of exhaustion) and an independent algebraic generalization approach are provided. Applications provided as examples include use of the formula to generate new series for common functions as well as computing the group velocity distribution resulting from waves diffracted from an aperture.

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