Integration in finite terms and simplification with dilogarithms: A progress report. (English) Zbl 0688.12016
Computers and mathematics, Proc. Conf., Cambridge/Mass. 1989, 166-171 (1989).
Summary: [For the entire collection see Zbl 0671.00018.]
In this extended abstract, we report on a new theorem that generalizes Liouville’s theorem on integration in finite terms. The new theorem allows dilogarithms to occur in the integral in addition to elementary functions. The proof is based on two identities, for the dilogarithm, that characterize all the possible algebraic relations among dilogarithms of functions that are built up from the rational functions by taking transcendental exponentials, dilogarithms, and logarithms. We report also on a generalization of Risch’s decision procedure for integrating elementary transcendental functions to include dilogarithms and elementary functions in the integral.
In this extended abstract, we report on a new theorem that generalizes Liouville’s theorem on integration in finite terms. The new theorem allows dilogarithms to occur in the integral in addition to elementary functions. The proof is based on two identities, for the dilogarithm, that characterize all the possible algebraic relations among dilogarithms of functions that are built up from the rational functions by taking transcendental exponentials, dilogarithms, and logarithms. We report also on a generalization of Risch’s decision procedure for integrating elementary transcendental functions to include dilogarithms and elementary functions in the integral.
