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RATIONAL APPROXIMATIONS TO VALUES OF BELL POLYNOMIALS AT POINTS INVOLVING EULER’S CONSTANT AND ZETA VALUES

Part of: Computational aspects Diophantine approximation, transcendental number theory Zeta and $L$-functions: analytic theory Sequences and sets

Published online by Cambridge University Press:  15 June 2012

KH. HESSAMI PILEHROOD  and
T. HESSAMI PILEHROOD
KH. HESSAMI PILEHROOD
Affiliation:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5 (email: hessamik@gmail.com)
T. HESSAMI PILEHROOD*
Affiliation:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5 (email: hessamit@gmail.com)
*
✉For correspondence; e-mail: hessamit@gmail.com
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Abstract

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In this paper we present new explicit simultaneous rational approximations which converge subexponentially to the values of the Bell polynomials at the points where m=1,2,…,a, a∈ℕ, γ is Euler’s constant and ζ is the Riemann zeta function.

Keywords

Euler constantzeta valueBell polynomialBernoulli polynomialMeijer G-functionrational approximationsaddle point method

MSC classification

Secondary: 11J13: Simultaneous homogeneous approximation, linear forms 11B68: Bernoulli and Euler numbers and polynomials 11M35: Hurwitz and Lerch zeta functions 33F10: Symbolic computation (Gosper and Zeilberger algorithms, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 92 , Issue 1 , February 2012 , pp. 71 - 98
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

This research was in part supported by grants no. 89110024 (first author) and no. 89110025 (second author) from the School of Mathematics, Institute for Research in Fundamental Sciences (IPM).

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