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.

中文翻译：

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初等超几何函数、Heun 函数和 MKZ 算子的矩

我们考虑一些超几何函数并证明它们是初等函数。因此，Meyer-Konig 和 Zeller 类型算子的二阶矩是初等函数。这些算子的高阶矩用初等函数和多对数表示。其他应用涉及在基本超几何函数的级数或有限和中展开某些 Heun 函数。