# Tagged Questions

**14**

votes

**1**answer

322 views

### Is this combination of generalized polygamma and dilogarithm actually zero? $\Im\;\psi^{(-2)}(1+i)+\frac1{4\pi}\text{Li}_2(e^{-2\pi})-\log\sqrt{2\pi}+\frac{5\pi}{24}+\frac12$

I encountered this quantity in my calculations and tried to simplify it. Approximate numeric calculations suggested it could be zero (more precisely, it is certainly less than $10^{-4\times10^3}$ in ...

**5**

votes

**5**answers

722 views

### Summation of an expression

Hi,
Does anyone have an idea about an exact or approximate formulae for the following summation?
$$
\sum_{j=1}^n \frac{j^k}{(j-1)!}
$$
where k is a positive integer (the denominator of the j^th term ...

**0**

votes

**1**answer

779 views

### Generalizations of a product formula for the gamma function

Hello and Happy holidays.
I am interested in generalizations of the following product formula for the gamma function
$\Gamma(z)= \int_{0}^{\infty} t^{z-1}e^{-t}dt$ when $n \geq 2$:
\begin{align}
...

**2**

votes

**0**answers

341 views

### Can any antidifference (indefinite sum) of a function be expressed in elementary functions and generalized polygamma function if its integral can be expressed in elementary functions?

If the integral or multiplicative integral of a function can be expressed with elementary functions, does it mean its indefinite sum (antidifference) or indefinite product respectively can be ...

**5**

votes

**2**answers

1k views

### Multiplicative integral of $\Gamma(x)$

A recent question on the notion and notation of multiplicative integrals
( What is the standard notation for a multiplicative integral? ) induced me to play with the Riemann products of the Gamma ...