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http://functions.wolfram.com/10.06.20.0001.01
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D[LerchPhiClassical[z, s, a], z] ==
(1/z) (LerchPhiClassical[z, s - 1, a] - a LerchPhiClassical[z, s, a])
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Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", "s", ",", "a"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", "z"], RowBox[List["(", RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", RowBox[List["s", "-", "1"]], ",", "a"]], "]"]], "-", RowBox[List["a", " ", RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", "s", ",", "a"]], "]"]]]]]], ")"]]]]]]]]
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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> <mfrac> <mrow> <mo> ∂ </mo> <semantics> <mrow> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mi> a </mi> </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["a", Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2, $CellContext`e3], LerchPhi[$CellContext`e1, $CellContext`e2, $CellContext`e3]]]] </annotation> </semantics> </mrow> <mrow> <mo> ∂ </mo> <mi> z </mi> </mrow> </mfrac> <mo> ⩵ </mo> <mfrac> <mrow> <semantics> <mrow> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mrow> <mi> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[OverscriptBox["\[CapitalPhi]", "^"], "(", RowBox[List[TagBox["z", Rule[Editable, True]], ",", TagBox[RowBox[List["s", "-", "1"]], Rule[Editable, True]], ",", TagBox["a", Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2, $CellContext`e3], LerchPhi[$CellContext`e1, $CellContext`e2, $CellContext`e3]]]] </annotation> </semantics> <mo> - </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <semantics> <mrow> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mi> a </mi> </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["a", Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2, $CellContext`e3], LerchPhi[$CellContext`e1, $CellContext`e2, $CellContext`e3]]]] </annotation> </semantics> </mrow> </mrow> <mi> z </mi> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> LerchPhi </ci> <ci> z </ci> <ci> s </ci> <ci> a </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> LerchPhi </ci> <ci> z </ci> <apply> <plus /> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <ci> LerchPhi </ci> <ci> z </ci> <ci> s </ci> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["LerchPhiClassical", "[", RowBox[List["z_", ",", "s_", ",", "a_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", RowBox[List["s", "-", "1"]], ",", "a"]], "]"]], "-", RowBox[List["a", " ", RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", "s", ",", "a"]], "]"]]]]]], "z"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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