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arXiv:1501.00740 [math.NT]AbstractReferencesReviewsResources

Expansions of the generalized Euler's constants into the series of polynomials in $π^{-2}$ and into the formal enveloping series with rational coefficients only

Iaroslav V. Blagouchine

Published 2015-01-05Version 1

Two new series expansions for the m-th generalized Euler's constant (Stieltjes constants) are obtained. The first expansion involves Stirling numbers of the first kind and contains polynomials in 1/pi^2 with rational coefficients. The second expansion is a formal divergent enveloping series with rational coefficients only. This expansion is particularly simple and involve Bernoulli numbers with a nonlinear combination of generalized harmonic numbers.

Categories: math.NT, math.CO, math.CV
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