Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











variants of this functions
EllipticThetaPrime






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.05.06.0007.01









  


  










Input Form





EllipticThetaPrime[1, z, q] \[Proportional] EllipticThetaPrime[1, z, Subscript[q, 0]] + Derivative[0, 1, 1][EllipticTheta][1, z, Subscript[q, 0]] (q - Subscript[q, 0]) + (1/2) Derivative[0, 1, 2][EllipticTheta][1, z, Subscript[q, 0]] (q - Subscript[q, 0])^2 + (1/6) Derivative[0, 1, 3][EllipticTheta][1, z, Subscript[q, 0]] (q - Subscript[q, 0])^3 + O[(q - Subscript[q, 0])^4]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z", ",", SubscriptBox["q", "0"]]], "]"]], "+", " ", RowBox[List[RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "1", ",", "1"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["1", ",", "z", ",", SubscriptBox["q", "0"]]], "]"]], RowBox[List["(", RowBox[List["q", "-", SubscriptBox["q", "0"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "1", ",", "2"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["1", ",", "z", ",", SubscriptBox["q", "0"]]], "]"]], SuperscriptBox[RowBox[List["(", RowBox[List["q", "-", SubscriptBox["q", "0"]]], ")"]], "2"]]], " ", "+", RowBox[List[FractionBox["1", "6"], " ", RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "1", ",", "3"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["1", ",", "z", ",", SubscriptBox["q", "0"]]], "]"]], SuperscriptBox[RowBox[List["(", RowBox[List["q", "-", SubscriptBox["q", "0"]]], ")"]], "3"]]], "+", RowBox[List["O", "[", SuperscriptBox[RowBox[List["(", RowBox[List["q", "-", SubscriptBox["q", "0"]]], ")"]], "4"], "]"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <semantics> <mi> &#977; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[CurlyTheta]&quot;, EllipticThetaPrime] </annotation> </semantics> <mn> 1 </mn> <mo> &#8242; </mo> </msubsup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <msubsup> <semantics> <mi> &#977; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[CurlyTheta]&quot;, EllipticThetaPrime] </annotation> </semantics> <mn> 1 </mn> <mo> &#8242; </mo> </msubsup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mtext> </mtext> <mrow> <mrow> <msubsup> <mi> &#977; </mi> <mn> 1 </mn> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> </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> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <msubsup> <mi> &#977; </mi> <mn> 1 </mn> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> </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> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mtext> </mtext> <msup> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mtext> </mtext> <mrow> <msubsup> <mi> &#977; </mi> <mn> 1 </mn> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 3 </mn> </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> <mn> 6 </mn> </mfrac> <mo> &#8290; </mo> <mtext> </mtext> <msup> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msubsup> <semantics> <mi> &#977; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[CurlyTheta]&quot;, EllipticThetaPrime] </annotation> </semantics> <mn> 1 </mn> <mo> &#8242; </mo> </msubsup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <msubsup> <semantics> <mi> &#977; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[CurlyTheta]&quot;, EllipticThetaPrime] </annotation> </semantics> <mn> 1 </mn> <mo> &#8242; </mo> </msubsup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mtext> </mtext> <mrow> <mrow> <msubsup> <mi> &#977; </mi> <mn> 1 </mn> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> </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> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <msubsup> <mi> &#977; </mi> <mn> 1 </mn> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> </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> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mtext> </mtext> <msup> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mtext> </mtext> <mrow> <msubsup> <mi> &#977; </mi> <mn> 1 </mn> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 3 </mn> </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> <mn> 6 </mn> </mfrac> <mo> &#8290; </mo> <mtext> </mtext> <msup> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <msub> <mi> q </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z_", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z", ",", SubscriptBox["qq", "0"]]], "]"]], "+", RowBox[List[RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "1", ",", "1"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["1", ",", "z", ",", SubscriptBox["qq", "0"]]], "]"]], " ", RowBox[List["(", RowBox[List["q", "-", SubscriptBox["qq", "0"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "1", ",", "2"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["1", ",", "z", ",", SubscriptBox["qq", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["q", "-", SubscriptBox["qq", "0"]]], ")"]], "2"]]], "+", RowBox[List[FractionBox["1", "6"], " ", RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "1", ",", "3"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["1", ",", "z", ",", SubscriptBox["qq", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["q", "-", SubscriptBox["qq", "0"]]], ")"]], "3"]]], "+", SuperscriptBox[RowBox[List["O", "[", RowBox[List["q", "-", SubscriptBox["qq", "0"]]], "]"]], "4"]]]]]]]










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





2007-05-02





© 1998- Wolfram Research, Inc.