论文标题
退化的多指数函数和退化的钟形多项式
Degenerate polyexponential functions and degenerate Bell polynomials
论文作者
论文摘要
近年来，研究了一些特殊多项式的退化版本，这是由卡利茨（Carlitz）在研究退化的伯努利（Bernoulli）和欧拉（Euler）多项式的研究中启动的，重新获得了数学的生动兴趣。在本文中，作为Hardy引入的多指数函数的退化版本，我们研究了退化的多指数函数，并得出了它们的各种特性。此外，我们引入了新型的退化钟形多项式，这与先前研究的部分退化的钟形多项式不同，并且在最近对退化零截断的poissonrandom变量的研究中自然出现，并推断出其某些特性。此外，我们得出了连接多指数函数和新类型退化钟形多项式的一些身份。
I recent years, studying degenerate versions of some special polynomials, which was initiated by Carlitz in an investigation of the degenerate Bernoulli and Euler polynomials, regained lively interest of mant mathematicains. In this paper, as a degenerate version of polyexponential functions introduced by Hardy, we study degenerate polyexponential functions and derive various properties of them. Also, we introduce new type degenerate Bell polynomials, which are different from the previous studied partially degenerate Bell polynomials and arise naturally in the recent study of degenerate zero-truncated Poissonrandom variables, and deduce some of their properties. Furthermore, we derive some identities connecting the polyexponential functions and the new type degenerate Bell polynomials.
