Karen T. Kohl
Abstract
In spite of being a classical problem, the current techniques available for Symbolic Integration are not sufficient to evaluate a variety of integrals coming from Mathematical Physics, such as Bessel functions. The Method of Brackets [2, 3], a heuristic process appearing in the evaluation of Feynman diagrams, can be used to evaluate symbolically a large class of single or multiple integrals. It represents an extension of the so-called Ramanujan Master Theorem [1]. The first implementation of the Method of Brackets has been written by the author in the open-source computer algebra system Sage. This implementation allows experimentation with representations of the integrand, which can affect output and efficiency. An algorithm that chooses the best representation of the integrand is being developed.
- T. Amdeberhan, O. Espinosa, I. Gonzalez, M. Harrison, V. H. Moll, and A. Straub. Ramanujan Master Theorem. In progress.Google Scholar
- I. Gonzalez and V. Moll. Definite integrals by the method of brackets. Part 1. Advances in Applied Mathematics 45, 2010, 50--73.Google ScholarDigital Library
- I. Gonzalez, V. Moll, and A. Straub. The method of brackets. Part 2: Examples and Applications. Contemporary Mathematics, volume 517, 2010, pages 157--171.Google ScholarCross Ref
- I. S. Gradshteyn and I. M. Ryzhik. Table of Integrals, Series, and Products. Edited by A. Jeffrey and D. Zwillinger. Academic Press, New York, 7th edition, 2007.Google Scholar
Index Terms
- An implementation of the method of brackets for symbolic integration
Recommendations
Symbolic integration: the stormy decade
Three approaches to symbolic integration in the 1960's are described. The first, from artificial intelligence, led to Slagle's SAINT and to a large degree to Moses' SIN. The second, from algebraic manipulation, led to Manove's implementation and to ...
Symbolic Integration of Hyperexponential 1-Forms
ISSAC '19: Proceedings of the 2019 on International Symposium on Symbolic and Algebraic ComputationLet H be a hyperexponential function in n variables x=(x1,…,xn) with coefficients in a field ℚ , [ℚ :ℚ ] < ∞, and ω a rational differential 1-form. Assume that Hømega is closed and H transcendental. We prove using Schanuel conjecture that there exist a ...
Symbolic-numeric Gaussian cubature rules
It is well known that Gaussian cubature rules are related to multivariate orthogonal polynomials. The cubature rules found in the literature use common zeroes of some linearly independent set of products of basically univariate polynomials. We show how ...
Comments