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Results tagged with gamma-function
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user 10059
used only for functions based on gamma, not functions with some obscure relation to gamma
1
vote
Multiplicative integral of $\Gamma(x)$
Multiplicative integral of gamma function is
$$\int \Gamma(x)^{dx}=C e^{\psi^{(-2)}(x)}$$
if to use the popular generalization of polygamma function $\psi^{(p)}(z)$ put forward by Grossman in 1976. …
- 10.1k
0
votes
Formula for volume of $n$-ball for negative $n$
I want to make another answer to this question, although it is is not really an answer, and I do not know whether it is relevant or not, but it may be useful.
Let's take
$$V(n,R)=\frac{\pi^{\frac{n …
- 10.1k
5
votes
Formula for volume of $n$-ball for negative $n$
I will answer regarding the dimension $-1$.
An example of such space is a set of periodic lattices on a real line.
Indeed, you can see that the Hausdorff dimension of a periodic lattice is $-1$: If we …
- 10.1k
0
votes
Summation of an expression
You can use Wolfram Alpha to get exact solutions for different k, although the results are expressed in not-so-good functions
This allows to build smooth plots:
(both plots are for k=5)
- 10.1k
32
votes
Why is the Gamma function shifted from the factorial by 1?
They both are are equally "good". Unlike conventional calculus in discrete calculus there are two equally valid differentiation operators with little reason to prefere one over the other - forward dif …
- 10.1k