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Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions

2015

We construct several expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two variables of the first kind. The coefficients of different expansions obey four-, five-, or six-term recurrence relations that are reduced to ones involving less number of terms only in a few exceptional cases. The conditions for deriving finite-sum solutions via termination of the series are discussed.

Pure mathematicsRecurrence relationSeries (mathematics)Applied MathematicsLinear ordinary differential equationMathematics::Classical Analysis and ODEsFOS: Physical sciencesMathematical Physics (math-ph)symbols.namesake33E30 34B30 30BxxSpecial functionsMathematics - Classical Analysis and ODEssymbolsClassical Analysis and ODEs (math.CA)FOS: MathematicsBeta (velocity)Hypergeometric functionSeries expansionAnalysisBessel functionMathematical PhysicsMathematics
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