Integration in finite terms with special functions: A progress report

Abstract

Since R. Risch published an algorithm for calculating symbolic integrals of elementary functions in 1969, there has been an interest in extending his methods to include nonelementary functions. We report here on the recent development of two decision procedures for calculating integrals of transcendental elementary functions in terms of logarithmic integrals and error functions. Both of these algorithms are based on the Singer, Saunders, Caviness extension of Liouville's theorem on integration in finite terms [Ssc81]. Parts of the logarithmic integral algorithm have been implemented in Macsyma and a brief demonstration is given.KeywordsError FunctionElementary FunctionDecision ProcedureCharacteristic ZeroElementary FieldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.