Fungrim entry: ee3dc5

\psi\!\left(z\right) = \left(z - 1\right) \,{}_3F_2\!\left(1, 1, 2 - z, 2, 2, 1\right) - \gamma

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0

References:

http://functions.wolfram.com/GammaBetaErf/PolyGamma/26/01/01/0001/

TeX:

\psi\!\left(z\right) = \left(z - 1\right) \,{}_3F_2\!\left(1, 1, 2 - z, 2, 2, 1\right) - \gamma

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0

Definitions:

Fungrim symbol	Notation	Short description
`DigammaFunction`	$\psi\!\left(z\right)$	Digamma function
`ConstGamma`	$\gamma$	The constant gamma (0.577...)
`CC`	$\mathbb{C}$	Complex numbers
`Re`	$\operatorname{Re}(z)$	Real part

Source code for this entry:

Entry(ID("ee3dc5"),
    Formula(Equal(DigammaFunction(z), Sub(Mul(Sub(z, 1), Hypergeometric3F2(1, 1, Sub(2, z), 2, 2, 1)), ConstGamma))),
    Variables(z),
    Assumptions(And(Element(z, CC), Greater(Re(z), 0))),
    References("http://functions.wolfram.com/GammaBetaErf/PolyGamma/26/01/01/0001/"))

Topics using this entry

Digamma function