# Fungrim entry: 19e67f

$\sum_{n=A}^{B} \frac{1}{n + a} = \psi\!\left(a + B + 1\right) - \psi\!\left(a + A\right)$
Assumptions:$a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; A \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; B \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; A \le B \;\mathbin{\operatorname{and}}\; -a \notin \{A, A + 1, \ldots, B\}$
TeX:
\sum_{n=A}^{B} \frac{1}{n + a} = \psi\!\left(a + B + 1\right) - \psi\!\left(a + A\right)

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; A \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; B \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; A \le B \;\mathbin{\operatorname{and}}\; -a \notin \{A, A + 1, \ldots, B\}
Definitions:
Fungrim symbol Notation Short description
Sum$\sum_{n} f(n)$ Sum
DigammaFunction$\psi\!\left(z\right)$ Digamma function
CC$\mathbb{C}$ Complex numbers
ZZ$\mathbb{Z}$ Integers
Range$\{a, a + 1, \ldots, b\}$ Integers between given endpoints
Source code for this entry:
Entry(ID("19e67f"),
Assumptions(And(Element(a, CC), Element(A, ZZ), Element(B, ZZ), LessEqual(A, B), NotElement(Neg(a), Range(A, B)))))