Lerch transcendent: Specific values (formula 10.06.03.0071)

LerchPhi

$Mathematica Notation$

Zeta Functions and Polylogarithms

http://functions.wolfram.com/10.06.03.0071.01

Input Form

LerchPhiClassicalRegularized[z, 5, a] == HypergeometricPFQ[{1, a, a, a, a, a}, {1 + a, 1 + a, 1 + a, 1 + a, 1 + a}, z]/a^5

Standard Form

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MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mover> <mi> Φ </mi> <mo> ~ </mo> </mover> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mn> 5 </mn> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mi> a </mi> <mn> 5 </mn> </msup> </mfrac> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 6 </mn> </msub> <msub> <mi> F </mi> <mn> 5 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> a </mi> <mo> , </mo> <mi> a </mi> <mo> , </mo> <mi> a </mi> <mo> , </mo> <mi> a </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ; </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "6"], SubscriptBox["F", "5"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["a", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["a", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["a", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["a", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["a", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["a", "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["a", "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["a", "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["a", "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["a", "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> OverTilde </ci> <ci> Φ </ci> </apply> <ci> z </ci> <cn type='integer'> 5 </cn> <ci> a </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='integer'> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 1 </cn> <ci> a </ci> <ci> a </ci> <ci> a </ci> <ci> a </ci> <ci> a </ci> </list> <list> <apply> <plus /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </list> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2007-05-02