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http://functions.wolfram.com/09.08.20.0003.01
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D[EllipticThetaPrime[4, z, q], q] ==
4 Sum[(-1)^(k - 1) k^3 q^(k^2 - 1) Sin[2 k z], {k, 1, Infinity}] /;
Abs[q] < 1
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "q"], RowBox[List["EllipticThetaPrime", "[", RowBox[List["4", ",", "z", ",", "q"]], "]"]]]], "\[Equal]", RowBox[List["4", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["k", "-", "1"]]], " ", SuperscriptBox["k", "3"], " ", SuperscriptBox["q", RowBox[List[SuperscriptBox["k", "2"], "-", "1"]]], " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "k", " ", "z"]], "]"]]]]]]]]]], "/;", " ", RowBox[List[RowBox[List["Abs", "[", "q", "]"]], "<", "1"]]]]]]
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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> <mo> ∂ </mo> <mrow> <msubsup> <mi> ϑ </mi> <mn> 4 </mn> <mo> ′ </mo> </msubsup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <mi> q </mi> </mrow> </mfrac> <mo> ⩵ </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> k </mi> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> q </mi> <mrow> <msup> <mi> k </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> q </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> < </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> q </ci> </bvar> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <apply> <ci> Subscript </ci> <ci> ϑ </ci> <cn type='integer'> 4 </cn> </apply> </apply> <ci> z </ci> <ci> q </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> k </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> q </ci> <apply> <plus /> <apply> <power /> <ci> k </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <lt /> <apply> <abs /> <ci> q </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["q_"]]], RowBox[List["EllipticThetaPrime", "[", RowBox[List["4", ",", "z_", ",", "q_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["4", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["k", "-", "1"]]], " ", SuperscriptBox["k", "3"], " ", SuperscriptBox["q", RowBox[List[SuperscriptBox["k", "2"], "-", "1"]]], " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "k", " ", "z"]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "q", "]"]], "<", "1"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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