Elementary hypergeometric functions, Heun functions, and moments of MKZ operators
Ana Maria Acu, Ioan Rasa
TL;DR
This paper demonstrates that certain hypergeometric and Heun functions are elementary, and derives explicit formulas for moments of MKZ operators using elementary functions and polylogarithms.
Contribution
It shows that second order moments of MKZ operators are elementary functions and provides new expressions for higher order moments and Heun function expansions.
Findings
Second order moments of MKZ operators are elementary functions.
Higher order moments are expressed via elementary functions and polylogarithms.
Heun functions can be expanded into series or sums of elementary hypergeometric functions.
Abstract
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.
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