The integrals in Gradshteyn and Ryzhik. Part 35: Fixing the confusion of Φ and erf in the table

Abstract

The table of integrals by Gradshteyn and Ryzhik uses a large variety of special function. Some of them have very similar definitions. The different names have been kept because different users are accustomed to one name or the other. In occasion this leads to errors in the entries of the table. The error function, defined as the normalized primitive of exp(−x2), and a function denoted by Φ have very similar definitions. The goal of this note is to fix some entries that have appeared incorrectly in the current edition of the table.