# Tagged Questions

**5**

votes

**2**answers

748 views

### Is there a known formula for fractional derivative of cot x?

I wonder if there any established formula for fractional derivative of a function $\pi \cot (\pi x)$.
I derived the following expression:
$(\pi \cot (\pi ...

**5**

votes

**1**answer

408 views

### Is Zeta function discrete-analytic?

Let's define discrete-analytic functions as functions that are equal to their Newton series expansion:
$$f(x) = \sum_{k=0}^\infty \binom{x-a}k \Delta^k f(a)$$
My question is whether $\zeta(s,q)$ ...

**1**

vote

**0**answers

707 views

### Proof that derivative of Hurwitz Zeta by the first argument is not expressable in terms of Hurwitz Zeta

The set of elementary functions is defined so that it to be closed against operation of differentiation. It is also evidently close against discrete differentiation.
In the discrete calculus there is ...

**7**

votes

**4**answers

1k views

### Non-vanishing of zeta(s), Re(s)=1, without complex analysis?

Say you are allowed to use Fourier analysis, complex variables, Euler-Maclaurin, etc., but no complex analysis - no holomorphic continuations, no definition of analytic function, and, in particular, ...

**20**

votes

**3**answers

880 views

### Universality of zeta- and L-functions

VoroninĀ“s Universality Theorem (for the Riemann zeta-Function) according to Wikipedia: Let $U$ be a compact subset of the "critical half-strip" $\{s\in\mathbb{C}:\frac{1}{2}<Re(s)<1\}$ with ...