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arXiv · 0911.4731

Integral representations of the Legendre chi function

Djurdje Cvijović
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Abstract

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

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Djurdje Cvijović. 2009-11-29. Integral representations of the Legendre chi function. https://doi.org/10.1016/j.jmaa.2006.10.083

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