Fungrim entry: 686524

\psi\!\left(z\right) = -\gamma + \sum_{n=0}^{\infty} \left(\frac{1}{n + 1} - \frac{1}{n + z}\right)

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}

TeX:

\psi\!\left(z\right) = -\gamma + \sum_{n=0}^{\infty} \left(\frac{1}{n + 1} - \frac{1}{n + z}\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}

Definitions:

Fungrim symbol	Notation	Short description
`DigammaFunction`	$\psi\!\left(z\right)$	Digamma function
`ConstGamma`	$\gamma$	The constant gamma (0.577...)
`Sum`	$\sum_{n} f(n)$	Sum
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	Complex numbers
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n

Source code for this entry:

Entry(ID("686524"),
    Formula(Equal(DigammaFunction(z), Add(Neg(ConstGamma), Sum(Parentheses(Sub(Div(1, Add(n, 1)), Div(1, Add(n, z)))), For(n, 0, Infinity))))),
    Variables(z),
    Assumptions(And(Element(z, CC), NotElement(z, ZZLessEqual(0)))))

Topics using this entry

Digamma function