# Fungrim entry: b4825b

$\psi\!\left(-n + z\right) = -\frac{1}{z} + \psi\!\left(n + 1\right) + \sum_{k=1}^{\infty} \left({\left(-1\right)}^{k + 1} \zeta\!\left(k + 1\right) + \sum_{j=1}^{n} \frac{1}{{j}^{k + 1}}\right) {z}^{k}$
Assumptions:$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| < 1$
TeX:
\psi\!\left(-n + z\right) = -\frac{1}{z} + \psi\!\left(n + 1\right) + \sum_{k=1}^{\infty} \left({\left(-1\right)}^{k + 1} \zeta\!\left(k + 1\right) + \sum_{j=1}^{n} \frac{1}{{j}^{k + 1}}\right) {z}^{k}

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| < 1
Definitions:
Fungrim symbol Notation Short description
DigammaFunction$\psi\!\left(z\right)$ Digamma function
Sum$\sum_{n} f(n)$ Sum
Pow${a}^{b}$ Power
RiemannZeta$\zeta\!\left(s\right)$ Riemann zeta function
Infinity$\infty$ Positive infinity
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
CC$\mathbb{C}$ Complex numbers
Abs$\left|z\right|$ Absolute value
Source code for this entry:
Entry(ID("b4825b"),
Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(z, CC), Less(Abs(z), 1))))