Some remarks, generalizations and misprints in the integrals in Gradshteyn and Ryzhik

Abstract

This paper presents some remarks, generalizations and misprints to the classic table of integrals of Gradshteyn and Ryzhik. It is noted that the conditions for convergence in a number of integrals, that in the original source were obtained via Bessel transforms, are too restrictive. Also, a property of the parabolic cylinder function is used to simplify one of the integrals in Gradshteyn and Ryzhik into a result that enables the calculation of integrals for squares and higher powers of the error function. Subsequently, an indefinite integral for the normal distribution is specialized into several expressions that are reported in Gradshteyn and Ryzhik. The paper ends by listing integrals for which the aforementioned overly restrictive conditions emerge and/or for which generalizations or misprints are found