A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments
Yuewu Li, Feng Qi
Abstract
In this paper, the authors briefly review some closed-form formulas of the Gauss hypergeometric function at specific arguments, alternatively prove four of these formulas, newly extend a closed-form formula of the Gauss hypergeometric function at some specific arguments, successfully apply a special case of the newly extended closed-form formula to derive an alternative form for the Maclaurin power series expansion of the Wilf function, and discover two novel increasing rational approximations to a quarter of the circular constant.
Topics & Concepts
Hypergeometric functionGaussHypergeometric function of a matrix argumentMathematicsConfluent hypergeometric functionBasic hypergeometric seriesGeneralized hypergeometric functionPure mathematicsLauricella hypergeometric seriesBilateral hypergeometric seriesHypergeometric identityFunction (biology)Hypergeometric distributionAlgebra over a fieldPhysicsBiologyQuantum mechanicsEvolutionary biologyMathematical functions and polynomialsAdvanced Mathematical IdentitiesMathematics and Applications