# Tagged Questions

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

203 views

190 views

### What is the correct differential equation for the Laguerre function?

I would like to derive the correct Laguerre function from the differential equation but the differential equations seems different from the original one. What is the correct differential equation and ...
88 views

709 views

248 views

536 views

### Does $\left(n^2 \sin n\right)$ have a convergent subsequence?

I'm wrestling with the following: Question: For what values of $\alpha > 0$ does the sequence $\left(n^\alpha \sin n\right)$ have a convergent subsequence? (The special case $\alpha = 2$ in ...
197 views

### Infinite series representation. Limited or not?

Recently I've found the following. Let $n < m$. Then the integral $$\int\limits_0^\infty {\frac{{{x^{n-1}}}}{{1 + {x^m}}}} dx$$ converges and its value is (using the $B$ and $\Gamma$ function ...
594 views

307 views

135 views

### How to find a function with the following properties?

I want to find a function $f(s,x)$ such that $f(s,x)$ is analytic for any $s \in Z^+$, $f(s,x)=B_s(x)$, where $B_s(x)$ are the Bernoulli polynomials $f(a, x)$ is elementary against $x$ at any ...
227 views

### Can we confirm $\sum_x{x!}$?
According to Wikipedia's article on indefinite sums, they list the following formula near the bottom of the page: $$\displaystyle \sum_x{\Gamma(x)}=(-1)^{x+1}\Gamma(x)\frac{\Gamma(1-x,-1)}{e}+C$$ ...