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questions
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votes
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How to prove $\int_0^\infty e^{-a q} \Gamma (0,q)^2 \, dq = -\frac{1}{a}\left(2 \operatorname{Li}_2(-a-1)+\frac{\pi ^2}{6}\right)$
In my study (https://math.stackexchange.com/a/3392284/198592) of pdfs for the harmonic mean of $n$ independent random variables $x_{i} \sim U(0,1)$ I discovered the lemma
$$f_{2}(a) = \int_0^{\infty }...
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5
votes
1
answer
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How prime numbers are related to special functions?
We know that the Riemann zeta function is defined as
$$\zeta(s)=\sum_{n=1}^\infty\frac{1}{n^s},$$
for all $\Re(s)>1$.
Because of Euler product formula we also know that
$$\zeta(s) = \sum_{n=1}^\...
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