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http://functions.wolfram.com/10.06.16.0009.01
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LerchPhiClassical[z, s, 2 a] == (LerchPhiClassical[z^2, s, a] +
z LerchPhiClassical[z^2, s, a + 1/2])/2^s
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Cell[BoxData[RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", "s", ",", RowBox[List["2", "a"]]]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List["-", "s"]]], RowBox[List["(", RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List[SuperscriptBox["z", "2"], ",", "s", ",", "a"]], "]"]], "+", RowBox[List["z", " ", RowBox[List["LerchPhiClassical", "[", RowBox[List[SuperscriptBox["z", "2"], ",", "s", ",", RowBox[List["a", "+", FractionBox["1", "2"]]]]], "]"]]]]]], ")"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[OverscriptBox["\[CapitalPhi]", "^"], "(", RowBox[List[TagBox["z", Rule[Editable, True]], ",", TagBox["s", Rule[Editable, True]], ",", TagBox[RowBox[List["2", "a"]], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[List[$CellContext`a, $CellContext`b, $CellContext`c], LerchPhi[$CellContext`a, $CellContext`b, $CellContext`c]]]] </annotation> </semantics> <mo>  </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LerchPhi </ci> <ci> z </ci> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <apply> <plus /> <apply> <apply> <ci> OverHat </ci> <ci> Φ </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <ci> s </ci> <ci> a </ci> </apply> <apply> <times /> <ci> z </ci> <apply> <apply> <ci> OverHat </ci> <ci> Φ </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <ci> s </ci> <apply> <plus /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LerchPhiClassical", "[", RowBox[List["z_", ",", "s_", ",", RowBox[List["2", " ", "a_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List["-", "s"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List[SuperscriptBox["z", "2"], ",", "s", ",", "a"]], "]"]], "+", RowBox[List["z", " ", RowBox[List["LerchPhiClassical", "[", RowBox[List[SuperscriptBox["z", "2"], ",", "s", ",", RowBox[List["a", "+", FractionBox["1", "2"]]]]], "]"]]]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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