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variants of this functions
EllipticTheta




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[1,z,q] > Series representations > q-series > Expansions at generic point q==q0





http://functions.wolfram.com/09.01.06.0033.01









  


  








Input Form





EllipticTheta[1, z, q] \[Proportional] EllipticTheta[1, z, Subscript[q, 0]] (1 + O[q - Subscript[q, 0]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", SubscriptBox["q", "0"]]], "]"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["q", "-", SubscriptBox["q", "0"]]], "]"]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <ci> z </ci> <ci> q </ci> </apply> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> q </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> q </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z_", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", SubscriptBox["qq", "0"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["q", "-", SubscriptBox["qq", "0"]]], "]"]]]], ")"]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2007-05-02