legendre chi function

In mathematics, the Legendre chi function is defined as

\chi_n(z) = \sum_{k=0}^\infty \frac{z^{2k+1}}{(2k+1)^n}. The discrete fourier transform of the Legendre chi function with respect to the order n is the Hurwitz zeta function (Cvijovic). The Legendre chi function is a special case of the Lerch Transcendent, and is given by

\chi_n(z)=2^{-n}z\,\Phi (z^2,n,1/2)\,

References

Djurdje Cvijovic and Jacek Klinowski. Math. Comp. 68 (1999), 1623-1630, 1999. (abstract)

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