Question

What is the limit $\lim_{x\to 0}\left(\frac{x!x!!!x!!!!!...}{x!!x!!!!x!!!!!!...}\right)^{-\frac{1}{x}}=^?$

score 135 · Answer 1 · 2026-03-30 07:56:05

135

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What is the limit $\lim_{x\to 0}\left(\frac{x!x!!!x!!!!!...}{x!!x!!!!x!!!!!!...}\right)^{-\frac{1}{x}}=^?$

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122

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List Question

What is the limit $\lim_{x\to 0}\left(\frac{x!x!!!x!!!!!...}{x!!x!!!!x!!!!!!...}\right)^{-\frac{1}{x}}=^?$

evaluate beta function

Inequality including the minimum value of the Gamma function and the Champernowne constant .

$\lim\limits_{m\to 0}\dfrac{{}_1F_2\left(-\frac 12;\frac 12,\frac m2;x\right)}{\Gamma(m)}$

New formula like Stirling formula for product of Gamma function :$ \left(x!\right)\left(\frac{1}{x}\right)!$?

Definite integral by Malmsten's formula

Is there any closed form for the integral $\int_0^{\frac{\pi}{2}} \frac{\ln ^n(\sin x) \ln ^m(\cos x)}{\tan x} d x?$

Generalizing an incomplete Gamma function to many variables.

Multiple integral involving exponential function

A method for approximating a hypergeometric function to an elementary function

Generalizing $\sum_{n=1}^\infty \frac{\Gamma(n)\Gamma(x)}{\Gamma(n+x)} = \frac1{x-1}$ to double sum

Computing a specific integral and expressing it in terms of the Gamma function

What's special about $\zeta(x)\Gamma(x/2+1)$?

Cosine Function As Infinite Product

Is there some collection of popular non-gamma functions interpolating the factorial?

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