Beyond the Beta Integral Method: Transformation Formulas for Hypergeometric Functions via Meijer’s G Function
Dmitrii Karp, E. G. Prilepkina
Abstract
The beta integral method proved itself as a simple but nonetheless powerful method for generating hypergeometric identities at a fixed argument. In this paper, we propose a generalization by substituting the beta density with a particular type of Meijer’s G function. By the application of our method to known transformation formulas, we derive about forty hypergeometric identities, the majority of which are believed to be new.
Topics & Concepts
MathematicsTransformation (genetics)Beta function (physics)BETA (programming language)Hypergeometric functionBarnes integralFunction (biology)Generalized hypergeometric functionPure mathematicsApplied mathematicsPhysicsHypergeometric function of a matrix argumentComputer scienceRelationship between string theory and quantum field theoryQuantum gravityChemistryQuantumGeneBiochemistryBiologyProgramming languageEvolutionary biologyQuantum mechanicsMathematical functions and polynomialsIterative Methods for Nonlinear EquationsAdvanced Mathematical Identities