9405068 Caviness The research to be carried out is in the general area of algorithms for integration in finite terms (that is, indefinite or symbolic integration) with particular emphasis on the development and implementation of algorithms involving special functions. In the last few decades substantial progress has been made on algorithms for integration in finite terms. Risch's work culminated more than a century of work on integration of elementary functions. Almost immediately attention turned to integration involving larger classes of functions including special functions. The first real advance in this area was the extension of the Liouville theorem for a class of special functions by Singer, Saunders, and Caviness upon which Cherry and Knowles developed algorithms for integrating integrands containing error functions and logarithmic integrals in terms of such. This work however did not cover the important dilogarithms and associated functions that occur in many applications. Baddoura's work has given an elegant way to integrate in terms of the dilogarithm. This project will continue this line of research. The overall objective is to implement the algorithms obtained and to improve and extend their scope for integration of and in terms of various special functions. ***
