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Series and product representations for some mathematical constants

Authors:

Horst Alzer Stamatis Koumandos

Affiliation:

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

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

where S(m) = ∑_k=1^∞ 1/2^k+m.

Keywords:

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

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