# Questions tagged [gamma-function]

Questions on the gamma function $\Gamma(z)$ of Euler extending the usual factorial $n!$ for arbitrary argument, and related functions. The Gamma function is a specific way to extend the factorial function to other values using integrals.

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### Integral over a product of polynomial, exponential and Bessel function

In a physics textbook I'm working through I found an interesting integral identity which I want to prove: \begin{equation} \int_0^\infty t^{\nu +1} J_\nu(\beta t) e^{-\alpha t} \, dt = \frac{2\alpha (...
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### Series with poles of Gamma function

So I have a series: $\sum_{n=0}^\infty \frac{x^n}{\Gamma(-n)}$. Can I just argue that $\lim_{n\to k} \frac{x^n}{\Gamma(-n)}$, $\forall k \in N_0$ is zero and thus the whole series becomes a null ...
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### Supremum or upper bound of bivariate function involving logarithms and combinatorial coefficients or the gamma function over a region of the integers

As I got no answers, I reposted this question in MO. I have been trying to find the supremum of this bivariate function over a specific region. However, the expressions that I get are horrible. I ...