Abstract
For second order linear ordinary differential equations with coefficients in C(x), we present an algorithm to reduce, whenever possible, the equation to an equation defined over a subfield of C(x). At the moment, we have implemented 2-descent, which means that if there exists a reduction to a subfield of index 2, then we can find it. If n is the number of true singularities, then 2-descent, if it exists, reduces the number of true singularities to at most n/2 + 2. In 12 out of the 17 examples sent to us by Bostan and Kauers, we found that repeated use of 2-descent reduced their regular singular equation down to 3 singularities, which means that 2-descent allows us to find 2F1-hypergeometric type solutions for about two third's of their equations.
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