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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Article dans une revue
Ramanujan Journal (The), 2017, 42 (1), pp.69-96 〈10.1007/s11139-015-9701-0 〉
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01429256
Contributeur : Christophe Vignat <>
Soumis le : samedi 7 janvier 2017 - 14:50:50
Dernière modification le : jeudi 5 avril 2018 - 12:30:05

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Adam 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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