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variants of this functions
EllipticTheta




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[1,z,q] > Identities involving the group of functions > Basic Algebraic Identities > Addition theorems > For mixed pairs





http://functions.wolfram.com/09.01.18.0034.01









  


  








Input Form





EllipticTheta[2, 0, q] EllipticTheta[4, 0, q] EllipticTheta[1, x + y, q] EllipticTheta[3, x - y, q] == EllipticTheta[1, x, q] EllipticTheta[3, x, q] EllipticTheta[2, y, q] EllipticTheta[4, y, q] + EllipticTheta[2, x, q] EllipticTheta[4, x, q] EllipticTheta[1, y, q] EllipticTheta[3, y, q]








Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> x </mi> <mo> + </mo> <mi> y </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> x </mi> <mo> - </mo> <mi> y </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> x </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mi> x </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mi> y </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mi> y </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mi> x </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mi> x </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> y </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mi> y </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> x </ci> <ci> y </ci> </apply> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <apply> <plus /> <ci> x </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> y </ci> </apply> </apply> <ci> q </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <ci> x </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <ci> x </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <ci> y </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <ci> y </ci> <ci> q </ci> </apply> </apply> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <ci> x </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <ci> x </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <ci> y </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <ci> y </ci> <ci> q </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29