Search results for "33E30"

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Elementary hypergeometric functions, Heun functions, and moments of MKZ operators

2019

We consider some hypergeometric functions and prove that they are elementary functions. Consequently, the second order moments of Meyer-Konig and Zeller type operators are elementary functions. The higher order moments of these operators are expressed in terms of elementary functions and polylogarithms. Other applications are concerned with the expansion of certain Heun functions in series or finite sums of elementary hypergeometric functions.

Pure mathematicsAlgebra and Number TheorySeries (mathematics)Applied Mathematics010102 general mathematicsMathematics::Classical Analysis and ODEsNumerical Analysis (math.NA)Type (model theory)33C05 33C90 33E30 41A3601 natural sciencesSecond order moments010101 applied mathematicsComputational MathematicsMathematics - Classical Analysis and ODEsClassical Analysis and ODEs (math.CA)FOS: MathematicsElementary functionHigher order momentsGeometry and TopologyMathematics - Numerical Analysis0101 mathematicsHypergeometric functionAnalysisMathematics
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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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