A procedure for proving special function inequalities involving a discrete parameter

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. Categories and Subject Descriptors

• Type: Conference
• Year: 2005
• Where: ISSAC
• Authors: Stefan Gerhold, Manuel Kauers
• Keywords: Cylindrical Algebraic Decomposition, ISSAC 2005, Proving Procedure, Special Function Inequalities