A procedure for proving special function inequalities involving a discrete parameter

Authors:
Stefan Gerhold;Manuel Kauers
Affiliations:
Johannes Kepler Universität, Linz, Austria;Johannes Kepler Universität, Linz, Austria
Venue:
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Year:
2005

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Abstract

We define a class of special function inequalities that contains many classical examples, such as the Cauchy-Schwarz inequality, and introduce a proving procedure based on induction and Cylindrical Algebraic Decomposition. We present an array of non-trivial examples that can be done by our method. Most of them have not been proven automatically before. Some difficult well-known inequalities such as the Askey-Gasper inequality and Vietoris's inequality lie in our class as well, but we do not know if our proving procedure terminates for them.