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http://functions.wolfram.com/09.01.06.0032.01
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EllipticTheta[1, z, q] ==
Sum[(Derivative[0, 0, k][EllipticTheta][1, z, Subscript[q, 0]]/k!)
(q - Subscript[q, 0])^k, {k, 0, Infinity}]
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Cell[BoxData[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[" ", RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "0", ",", "k"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["1", ",", "z", ",", SubscriptBox["q", "0"]]], "]"]]]], RowBox[List["k", "!"]]], SuperscriptBox[RowBox[List["(", RowBox[List["q", "-", SubscriptBox["q", "0"]]], ")"]], "k"]]]]]]]]]
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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> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <mfrac> <mrow> <mtext> </mtext> <mrow> <msubsup> <mi> ϑ </mi> <mn> 1 </mn> <mrow> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <mfrac> <mrow> <mtext> </mtext> <mrow> <msubsup> <mi> ϑ </mi> <mn> 1 </mn> <mrow> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z_", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "0", ",", "k"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["1", ",", "z", ",", SubscriptBox["qq", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["q", "-", SubscriptBox["qq", "0"]]], ")"]], "k"]]], RowBox[List["k", "!"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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