# Tagged Questions

Questions on special functions, useful functions that frequently appear in pure and applied mathematics (usually not including "elementary" functions).

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### Stirling's formula problem [on hold]

Use stirling's formula to find: $$\displaystyle \lim_{n\to \infty}\dfrac {\ln(n!)}{n\ln(n)}$$ .
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### Line in Modified Bessel Function of the First Kind

Plotting the modified Bessel function of the first kind $I_\nu(x)$ as a function of two real variables, it looks like to one side of $x=\frac{2}{3}\nu$ the function falls rapidly to zero and on the ...
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### Construct a master (possibly hypergeometric) formula from a family of formulas indexed by the half-integers and integers

I have a set of individual formulas ($a=1/2, 1, 3/2,\ldots,6$), each itself a function of an integer variable $k$, of increasing complexity. I would like to find a "master" formula (conjecturally of a ...
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### Help with an Incomplete Gamma function-like integral

I was working on some mathematical derivations where I was struck with integrals of the form given below: The integral seems very close to the incomplete gamma function integral. Note here that m ...