Modified Nörlund polynomials

详细信息    查看全文

• 作者：Atul Dixit ; Adam Kabza ; Victor H. Moll ; Christophe Vignat
• 关键词：Nörlund polynomials ; Square hyperbolic secant distribution ; Logarithmic moments ; Barnes zeta function ; Chebyshev polynomials ; Zagier polynomials
• 刊名：The Ramanujan Journal
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：42
• 期：1
• 页码：69-96
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Number Theory; Field Theory and Polynomials; Combinatorics; Fourier Analysis; Functions of a Complex Variable;
• 出版者：Springer US
• ISSN：1572-9303
• 卷排序：42

文摘

The modified Bernoulli numbers \(B_{n}^{*}\) considered by Zagier are generalized to modified Nörlund polynomials \({B_{n}^{(\ell )*}}\). For \(\ell \in \mathbb {N}\), an explicit expression for the generating function for these polynomials is obtained. Evaluations of some spectacular integrals involving Chebyshev polynomials and of a finite sum involving integrals of the Hurwitz zeta function are also obtained. New results about the \(\ell \)-fold convolution of the square hyperbolic secant distribution are obtained, such as a differential-difference equation satisfied by a logarithmic moment and a closed-form expression in terms of the Barnes zeta function.