Polygamma function: Primary definition (formula 06.15.02.0008)

PolyGamma

$Mathematica Notation$

Gamma, Beta, Erf

PolyGamma[nu,z]

Primary definition

http://functions.wolfram.com/06.15.02.0008.01

Input Form

PolyGamma[\[Nu], z] == D[PolyGamma[z], {z, \[Nu]}]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "\[Nu]"]], "}"]]], RowBox[List["PolyGamma", "[", "z", "]"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mi> ν </mi> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mfrac> <mrow> <msup> <mo> ∂ </mo> <mi> ν </mi> </msup> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> z </mi> <mi> ν </mi> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> PolyGamma </ci> <ci> ν </ci> <ci> z </ci> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <ci> ν </ci> </degree> </bvar> <apply> <ci> PolyGamma </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyGamma", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z", ",", "\[Nu]"]], "}"]]]]], RowBox[List["PolyGamma", "[", "z", "]"]]]]]]]]

Date Added to functions.wolfram.com (modification date)

2007-05-02

PolyGamma[z]