Related papers: The integrals in Gradshteyn and Ryzhik. Part 10: t…
We present a systematic derivation of some definite integrals in the classical table of Gradshteyn and Ryzhik that can be reduced to the gamma function.
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.
The classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik contains many definite integrals where the integrand is the product of a rational function times the logarithm of another rational function. We begin the systematic…
The table of Gradshteyn and Rhyzik contains some trigonometric integrals that can be expressed in terms of the beta function. We describe the evaluation of some of them.
The table of Gradshteyn and Ryzhik contains some integrals that can be expressed in terms of the incomplete beta function. We describe some elementary properties of this function and use them to check some of the formulas in the mentioned…
We present the evaluation of some logarithmic integrals. The integrand contains a rational function with complex poles. The methods are illustrated with examples found in the classical table of integrals by I. S. Gradshteyn and I. M.…
We present the evaluation of some definite integrals in the classical table by I. S. Gradshteyn and I. M. Ryzhik where the integrand is a combination of powers, exponentials and logarithms.
The classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik contains some elementary integrals. We discuss their evaluations.
We present the evaluation of a family of logarithmic integrals. This provides a unified proof of several formulas in the classical table of integrals by I. S. Gradshteyn and I. M. Rhyzik.
There have been many works on proving the integrals in the table of integrals compiled by Gradshteyn and Ryzhik, and in this paper we prove some doubly logarithmic integral identities in the Gradshteyn and Ryzhik table.
This paper considers various integrals where the integrand includes the log gamma function (or its derivative, the digamma function) multiplied by a trigonometric or hyperbolic function. Some apparently new integrals and series are…
The table of Gradshteyn and Ryzhik contains many entries that are related to elliptic integrals. We present a systematic derivation of some of them.
We consider several possible approaches to evaluating an integral involving the digamma function and a related logarithmic series.
The need to evaluate Logarithmic integrals is ubiquitous in essentially all quantitative areas including mathematical sciences, physical sciences. Some recent developments in Physics namely Feynman diagrams deals with the evaluation of…
We present evalauations and provide proofs of definite integrals involving the function x^p cos^n x. These formulae are generalizations of 3.761.11 and 3.822.1, among others, in the classical table of integrals by I. S. Gradshteyn and I. M.…
This paper considers some integrals where the integrand comprises the log gamma function or the digamma function multiplied by exponential or trigonometric functions.
The table of Gradshteyn and Ryzhik contains some integrals that can be reduced to the Frullani type. We present a selection of them.
The well known table of Gradshteyn and Ryzhik contains indefinite and definite integrals of both elementary and special functions. We give proofs of several entries containing integrands with some combination of hyperbolic and trigonometric…
We review a special technique for evaluating challenging integrals by providing a number of examples. Many of our examples prove integrals from the popular table of Gradshteyn and Ryzhik.
The logarithmic integral no. 4.325.7 from Gradshteyn and Ryzhik's tables of integrals was first evaluated by Malmst\'en. Recently, Blagouchine used contour integration methods to evaluate a family of logarithmic integrals that contains this…