Kim Taekyun, Kim Dae San
Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin, 300387 China ; Department of Mathematics, Kwangwoon University, Seoul, 139-701 Republic of Korea.
Department of Mathematics, Sogang University, Seoul, 121-742 Republic of Korea.
Springerplus. 2015 Oct 14;4:608. doi: 10.1186/s40064-015-1405-9. eCollection 2015.
The first degenerate version of the Bernoulli polynomials of the second kind appeared in the paper by Korobov (Math Notes 2:77-19, 1996; Proceedings of the IV international conference modern problems of number theory and its applications, pp 40-49, 2001). In this paper, we study two degenerate versions of the Bernoulli polynomials of the second kind which will be called Korobov polynomials of third kind and of the fourth kind. Some properties, identities, recurrence relations and connections with other polynomials are investigated by using umbral calculus.
第二类伯努利多项式的首个退化版本出现在科罗博夫的论文中（《数学笔记》2：77 - 19，1996；第四届国际数论及其应用现代问题会议论文集，第40 - 49页，2001）。在本文中，我们研究第二类伯努利多项式的两个退化版本，它们将被称为第三类和第四类科罗博夫多项式。利用符号演算研究了它们的一些性质、恒等式、递推关系以及与其他多项式的联系。
