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Series and product representations for some mathematical constants

Authors:

Horst Alzer Stamatis Koumandos

Institution:

1.Waldbr?l,Germany;2.Department of Mathematics and Statistics,The University of Cyprus,Nicosia,Cyprus

Abstract:

We present several series and product representations for γ, π, and other mathematical constants. One of our results states that, for all real numbers μ s>0, we have

$\gamma = \sum\limits_{k = 0}^\infty {\frac{1} {{(1 + \mu )^{k + 1} }}\sum\limits_{m = 0}^k {\left( {_m^k } \right)} \left( { - 1} \right)^m \mu ^{k - m} S(m),}$

where S(m) = ∑_k=1^∞ 1/2^k+m.

Keywords:

and phrases" target="_blank"> and phrases series representation product representation Euler’ s constant Catalan’ s constant Somos’ constant powers of π

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