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http://functions.wolfram.com/10.07.20.0007.01
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D[PolyLog[2, z], {z, m}] == Gamma[m]^2 Hypergeometric2F1Regularized[m, m,
1 + m, z] /; Element[m, Integers] && m > 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "m"]], "}"]]], RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z"]], "]"]]]], "\[Equal]", " ", RowBox[List[SuperscriptBox[RowBox[List["Gamma", "[", "m", "]"]], "2"], RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["m", ",", "m", ",", RowBox[List["1", "+", "m"]], ",", "z"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]
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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> <mrow> <mfrac> <mrow> <msup> <mo> ∂ </mo> <mi> m </mi> </msup> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> z </mi> <mi> m </mi> </msup> </mrow> </mfrac> <mo> ⩵ </mo> <mrow> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> m </mi> <mo> , </mo> <mi> m </mi> </mrow> <mo> ; </mo> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["m", Hypergeometric2F1Regularized, Rule[Editable, True]], ",", TagBox["m", Hypergeometric2F1Regularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["m", "+", "1"]], Hypergeometric2F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox["z", Hypergeometric2F1Regularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1Regularized] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> m </mi> <mo> ∈ </mo> <semantics> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> <annotation encoding='Mathematica'> TagBox[SuperscriptBox["\[DoubleStruckCapitalN]", "+"], Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <ci> m </ci> </degree> </bvar> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> Gamma </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1Regularized </ci> <ci> m </ci> <ci> m </ci> <apply> <plus /> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "m_"]], "}"]]]]], RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Gamma", "[", "m", "]"]], "2"], " ", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["m", ",", "m", ",", RowBox[List["1", "+", "m"]], ",", "z"]], "]"]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "0"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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