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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 > Four linear combinations of the fundamental identities





http://functions.wolfram.com/09.01.18.0069.01









  


  










Input Form





EllipticTheta[1, (1/2) (a + b + c + d), q] EllipticTheta[1, (1/2) (a + b - c - d), q] EllipticTheta[1, (1/2) (a - b + c - d), q] EllipticTheta[1, (1/2) (a - b - c + d), q] == (1/2) (EllipticTheta[1, a, q] EllipticTheta[1, b, q] EllipticTheta[1, c, q] EllipticTheta[1, d, q] - EllipticTheta[2, a, q] EllipticTheta[2, b, q] EllipticTheta[2, c, q] EllipticTheta[2, d, q] + EllipticTheta[3, a, q] EllipticTheta[3, b, q] EllipticTheta[3, c, q] EllipticTheta[3, d, q] - EllipticTheta[4, a, q] EllipticTheta[4, b, q] EllipticTheta[4, c, q] EllipticTheta[4, d, q])










Standard Form





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MathML Form







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</mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mi> a </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> b </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> c </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> d </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mi> a </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> b </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> c </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> d </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> a </ci> <ci> b </ci> <ci> c </ci> <ci> d </ci> </apply> </apply> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> </apply> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> </apply> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <ci> d </ci> </apply> </apply> <ci> q </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <ci> a </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <ci> b </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <ci> c </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <ci> d </ci> <ci> q </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <ci> d </ci> <ci> q </ci> </apply> </apply> </apply> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <ci> a </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <ci> b </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <ci> c </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <ci> d </ci> <ci> q </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <ci> a </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <ci> c </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <ci> d </ci> <ci> q </ci> </apply> </apply> </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





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