Computer Algebra Tools for Special Functions in Numerical Analysis (Subprojekt des DK W-1214)

We propose the development of computer algebra tools for special function manipulation. For many years the proposer's group has been working in this area; see the web page of the RISC Algorithmic Combinatorics group. Despite these efforts and other recent developments briefly described below, this research area is still in its early stage and much remains to be done. Being a subproject of the DK, particular emphasis will be put on tools that help in solving problems arising in numerical analysis. For example, in connection with hp finite element methods one typically encounters problems related to (multiple) definite integrals and inequalities involving special functions.