Symbolic computation of integrals by recurrence

Abstract

We discuss (1) the construction of recurrence formulas for several types of indefinite and definite integral, (2) the conversion of some of the recurrence schemes to general closed formulas, (3) the mechanization of these processes, (4) "vectorized" recurrence, (5) "telescoped" recurrence, (6) the outperformance of present automatic integration software by the procedures that use our formulas, and (7) the interface between symbolic computation (computer algebra) and mathematical discourse.