# Fungrim entry: 3ba544

$\frac{d}{d s}\, \zeta\!\left(s, a\right) = \zeta'\!\left(s, a\right)$
Assumptions:$s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; s \ne 1 \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(a) > 0$
TeX:
\frac{d}{d s}\, \zeta\!\left(s, a\right) = \zeta'\!\left(s, a\right)

s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; s \ne 1 \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(a) > 0
Definitions:
Fungrim symbol Notation Short description
ComplexDerivative$\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative
HurwitzZeta$\zeta\!\left(s, a\right)$ Hurwitz zeta function
CC$\mathbb{C}$ Complex numbers
Re$\operatorname{Re}(z)$ Real part
Source code for this entry:
Entry(ID("3ba544"),
Formula(Equal(ComplexDerivative(HurwitzZeta(s, a), For(s, s)), HurwitzZeta(s, a, 1))),
Variables(s, a),
Assumptions(And(Element(s, CC), NotEqual(s, 1), Element(a, CC), Greater(Re(a), 0))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC