Integral representations of the Legendre chi function

Details Integral representations of the Legendre chi function Integral representations of the Legendre chi function

2009-11-24

arxiv.org/abs/0911.4731v2

J. Math. Anal. Appl. 332 (2007) 1056-1062

Mathematics

Classical Analysis and ODEs

13 pages

Scientific paper

10.1016/j.jmaa.2006.10.083

We, by making use of elementary arguments, deduce integral representations of
the Legendre chi function $\chi_{s}(x)$ valid for $|z|<1$ and $\Re(s)>1$. Our
earlier established results on the integral representations for the Riemann
zeta function $\zeta(2 n+1)$ and the Dirichlet beta function $\beta(2 n)$ ,$
n\in\mathbb{N}$, are direct consequence of these representations.

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