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On a Ramanujan Type Entire Function and its Zeros
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2020-05-01 , DOI: 10.1016/j.jmaa.2020.123856
Dan Dai , Mourad E.H. Ismail , Xiang-Sheng Wang

Abstract In this paper, we derive some properties of a Ramanujan type entire function. A mild generalization of the Garret-Ismail-Stanton m-version of the Rogers-Ramanujan identities is obtained. Moreover, we investigate the zeros of the Ramanujan type entire function, and our results generalize those for the zeros of the Ramanujan function. Finally, an integral equation related to the Ramanujan type entire function is also derived.

中文翻译:

关于拉马努金型整个函数及其零点

摘要 在本文中,我们推导出了一个拉马努金型整函数的一些性质。获得了 Rogers-Ramanujan 恒等式的 Garret-Ismail-Stanton m 版本的温和概括。此外,我们研究了 Ramanujan 型整个函数的零点,我们的结果将这些推广到了 Ramanujan 函数的零点。最后,还推导出与拉马努金型整函数相关的积分方程。
更新日期:2020-05-01
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