On the Analytic Continuation of Lauricella–Saran Hypergeometric Function FK(a1,a2,b1,b2;a1,b2,c3;z)
Т. М. Antonova, Roman Dmytryshyn, Vitaliy Goran
Abstract
The paper establishes an analytical extension of two ratios of Lauricella–Saran hypergeometric functions FK with some parameter values to the corresponding branched continued fractions in their domain of convergence. The PC method used here is based on the correspondence between a formal triple power series and a branched continued fraction. As additional results, analytical extensions of the Lauricella–Saran hypergeometric functions FK(a1,a2,1,b2;a1,b2,c3;z) and FK(a1,1,b1,b2;a1,b2,c3;z) to the corresponding branched continued fractions were obtained. To illustrate this, we provide some numerical experiments at the end.
Topics & Concepts
Hypergeometric functionMathematicsLauricella hypergeometric seriesConvergence (economics)Pure mathematicsAppell seriesFunction (biology)Hypergeometric distributionExtension (predicate logic)ContinuationConfluent hypergeometric functionApplied mathematicsMathematical analysisComputer scienceHypergeometric function of a matrix argumentEconomicsEvolutionary biologyProgramming languageEconomic growthBiologyIterative Methods for Nonlinear EquationsMathematical functions and polynomialsOrbital Angular Momentum in Optics