Toward symbolic integration of elliptic integrals (Q1971734)

Integrals are considered of the form \(\int_y^x\prod_{i=1}^h(a_i+b_it)^{-1/2} \prod_{j=1}^n(a_j+b_jt)^{m_j} dt\), where \(h=3\) or \(4\), \(n\geq h\), the \(m\)'s are integers, and \(y<x\). A method is proposed by which this type of elliptic integrals can be integrated symbolically, without information regarding limits of integration and branch points of the integrand. The integral is expressed in terms of canonical \(R\)-functions [\textit{B. C. Carlson}, Numer. Algorithms 10, No. 1-2, 13-26 (1995; Zbl 0827.65024)]. Software is available at \url{http://www.neta.com/~cherry} or by e-mail at \url{cherry@neta.com}.