Integration in Finite Terms with Special Functions: The Logarithmic Integral

@article{Cherry1986IntegrationIF,
title={Integration in Finite Terms with Special Functions: The Logarithmic Integral},
author={G. W. Cherry},
journal={SIAM J. Comput.},
year={1986},
volume={15},
pages={1-21}
}

Since R. Risch published an algorithm for calculating symbolic integrals of elementary functions in 1969 (Traps. Amer. Math. Soc., 139 (1969), pp. 167–189), there has been an interest in extending his methods to include nonelementary functions. In this paper, we use the framework of differential algebra to make precise the notion of integration in terms of elementary functions and logarithmic integrals. Basing our work on a recent extension of Liouville’s theorem on integration in finite terms… Expand