Integration in finite terms with special functions: the error function (Q1071502)

A decision procedure for integrating a class of transcendental elementary functions in terms of elementary functions and error functions is described. The procedure consists of three mutually exclusive cases. In the first two cases a generalized procedure for completing squares is used to limit the error functions which can appear in the integral to a finite number. This reduces the problem to the solution of a differential equation and we use a result of \textit{R. H. Risch} [Trans. Am. Math. Soc. 139, 167-189 (1969; Zbl 0184.067)] to solve it. The third case can be reduced to the determination of what we have termed \(\Sigma\)- decompositions. The result presented here is the key procedure to a more general algorithm which is described fully in the author's Ph. D. thesis [Univ. Delaware (1983)].