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Modified Nörlund Polynomials

Abstract : 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.
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Contributor : Christophe Vignat <>
Submitted on : Saturday, January 7, 2017 - 2:50:50 PM
Last modification on : Wednesday, September 16, 2020 - 4:46:31 PM

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A. Kabza, Atul Dixit, Victor H. Moll, Christophe Vignat. Modified Nörlund Polynomials. Ramanujan Journal (The), 2017, 42 (1), pp.69-96. ⟨10.1007/s11139-015-9701-0⟩. ⟨hal-01429256⟩



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