The integrals in Gradshteyn and Ryzhik. Part 6: the beta function
Victor H. Moll
TL;DR
This paper reviews and evaluates a class of definite integrals from Gradshteyn and Ryzhik's table that can be expressed using the beta function, providing clarity and potential simplifications.
Contribution
It systematically connects a subset of integrals in Gradshteyn and Ryzhik to the beta function, enhancing understanding and computation methods.
Findings
Identifies integrals reducible to the beta function.
Provides explicit evaluation formulas for these integrals.
Simplifies the computation of certain definite integrals.
Abstract
We present the evaluation of definite integrals in the classical table by I. S. Gradshteyn and I. M. Ryzhik that can be reduced to the beta function.
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Taxonomy
TopicsMathematical functions and polynomials · Matrix Theory and Algorithms · Iterative Methods for Nonlinear Equations