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.
https://hal-centralesupelec.archives-ouvertes.fr/hal-01429256
Contributor : Christophe Vignat
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Submitted on : Saturday, January 7, 2017 - 2:50:50 PM
Last modification on : Monday, September 10, 2018 - 11:00:02 AM
