Lerch transcendent: Representations through equivalent functions (formula 10.06.27.0003)

LerchPhi

$Mathematica Notation$

Zeta Functions and Polylogarithms

LerchPhi[z,s,a]

Representations through equivalent functions

Interrelations

http://functions.wolfram.com/10.06.27.0003.01

Input Form

LerchPhi[z, 2 n, a] == LerchPhiClassical[z, 2 n, a] /; Element[n, Integers]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LerchPhi", "[", RowBox[List["z", ",", RowBox[List["2", "n"]], ",", "a"]], "]"]], "\[Equal]", RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", RowBox[List["2", "n"]], ",", "a"]], "]"]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <mi> Φ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[CapitalPhi]", "(", RowBox[List[TagBox["z", LerchPhi, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["2", " ", "n"]], LerchPhi, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["a", LerchPhi, Rule[Editable, True], Rule[Selectable, True]]]], ")"]], InterpretTemplate[Function[List[ZetaDump`e1$, ZetaDump`e2$, ZetaDump`e3$], LerchPhi[ZetaDump`e1$, ZetaDump`e2$, ZetaDump`e3$]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo>  </mo> <mrow> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> LerchPhi </ci> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <ci> a </ci> </apply> <apply> <apply> <ci> OverHat </ci> <ci> Φ </ci> </apply> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <ci> a </ci> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LerchPhi", "[", RowBox[List["z_", ",", RowBox[List["2", " ", "n_"]], ",", "a_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", RowBox[List["2", " ", "n"]], ",", "a"]], "]"]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]

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

2007-05-02