6 votes

What is the analytic continuation of a multifactorial?

Despite this being a 10-year old post, it does come up when searching "double factorial analytic continuation", so I thought I'd expand on Ted's answer. (I'm new to StackExchange so ...
Esran Douma's user avatar
2 votes
Accepted

Is the factorial of any number equal to zero?

Your question is flawed because factorial is only defined for $\mathbb{N}_0$. Since $0!=1$ and $\forall x\in\mathbb{N}_{>0}, x!>(x-1)!$, clearly there are no zeros. Desmos actually display the ...
IraeVid's user avatar
  • 2,638
2 votes

multifactorial of non-integer

Some years ago I calculated the equation of the multifactorial: $$z!_{(\alpha)}=\alpha^{\frac{z}{\alpha}}\Gamma\left(1+\frac{z}{\alpha}\right)\prod_{j=1}^{\alpha-1}\left(\frac{\alpha^{\frac{\alpha-j}{\...
Math Attack's user avatar
  • 2,343
1 vote

Sum of Hermite polynomials

With Mathematica: $$\sum _{n=0}^{\infty } \frac{w^n H_{2 n}(x)}{(1+2 n)!}=\frac{e^{x^2} \sqrt{\pi } \left(\text{erf}\left(\sqrt{w}-x\right)+\text{erf}\left(\sqrt{w}+x\right)\right)}{4 \sqrt{w}}$$
Mariusz Iwaniuk's user avatar

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