# Tagged Questions

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### Computing Reciprocal Gamma

Reciprocal Gamma $1/\Gamma(z)$ is an entire function and so it has a convergent Taylor series expansion which was given in its wikipedia article. ...
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Good day to everyone. In my scientific research I've got stuck with a contour integration problem. I would like to evaluate the following integral: $$I=\int_0^{\infty } \frac{e^{\frac{\alpha -\mathrm ... 0answers 183 views ### An integral with Gamma functions (Part 2) I was wondering if there is a generalization of the integral discussed here to a case like, \int \frac{d^dq}{q^{\nu_1}\vert \vec{q} \pm \vec{k}_1\vert ^{\nu_2}\vert \vec{q} \pm ... 0answers 129 views ### an infinite series expansion in terms of the polylogarithm function we have the complex valued function :$$f(z)=\sum_{n=0}^{\infty}a_{n}Li_{-n}(z)$$we wish to recover the coefficients a_{n} . the only thing i though would work is to try and come up with a function ... 1answer 442 views ### The zeros of the digamma function I wonder what work have been done on the zeros of the digamma function and on the values of the gamma function at such points (on the negative real axis). Any help please :) 0answers 293 views ### Why is Mellin-inverse of Gamma periodic? Specific Case The periodicity is obvious from computation:$$\cal{M}^{-1}\{\Gamma\}(x) := \frac{1}{2\pi i}\int_{c}\Gamma(s)x^{-s}d s=e^{-x} However, is there a way to see directly from the integral ...
I want to write the Bessel function of the first kind in polar coordinates $J_\alpha(z)=|J_\alpha(z)|e^{i\varphi_\alpha(z)}$ Is anything known about $\varphi_\alpha(z)$? In particular, I'm ...