arXiv subjects

Marc Prévost

Publications and source records attributed to Marc Prévost.

3 recordsLinked to original sources

arXiv2017

Recurrence relations for Apostol-Bernoulli , -Euler and -Genocchi polynomials of higher order

In \cite{luo2006,luosri2005}, Luo and Srivastava introduced some generalizations of the Apostol -Bernoulli polynomials and the Apostol-Euler polynomials. The main object of this paper is to extend the result of \cite{prevost2010} to these generalized polynomials. More precisely, using the Padé approximation of the exponential function, we obtain recurrence relations for Apostol-Bernoulli, Euler and also Genocchi polynomials of higher order. As an application we prove lacunary relation for some particular cases.

math.NT↗

arXiv2017

Remainder Padé approximants for the Hurwitz zeta function

Following our earlier research, we use the method introduced by the author in \cite{prevost1996} named Remainder Padé Approximant in \cite{rivoalprevost}, to construct approximations of the Hurwitz zeta function. We prove that these approximations are convergent on the positive real line. Applications to new rational approximations of $ζ(2)$ and $ζ(3)$ are given.

math.NA↗

arXiv2005

A family of criteria for irrationality of Euler's constant

Following earlier results of Sondow, we propose another criterion of irrationality for Euler's constant $γ$. It involves similar linear combinations of logarithm numbers $L\_{n,m}$. To prove that $γ$ is irrational, it suffices to prove that, for some fixed $m$, the distance of $d\_n L\_{n,m}$ ($d\_n$ is the least common multiple of the $n$ first integers) to the set of integers $\mathbf{Z}$ does not converge to 0. A similar result is obtained by replacing logarithms numbers by rational numbers: it gives a sufficient condition involving only rational numbers. Unfortunately, the chaotic behavior of $d\_n$ is an obstacle to verify this sufficient condition. All the proofs use in a large manner the theory of Padé approximation.

math.NT↗