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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=-15/4, b>=a > For fixed z and a=-15/4, b=21/4





http://functions.wolfram.com/07.23.03.abtw.01









  


  










Input Form





Hypergeometric2F1[-(15/4), 21/4, 5, -z] == (4096 Sqrt[2] (Sqrt[1 + z] (-29568 + 112112 z - 428967 z^2 + 2513973 z^3 + 69637504 z^4 + 188135424 z^5 + 180289536 z^6 + 58720256 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-29568 + 82544 z - 316855 z^2 + 2085006 z^3 + 72151477 z^4 + 257772928 z^5 + 368424960 z^6 + 239009792 z^7 + 58720256 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 4 (-7392 + 22484 z - 85701 z^2 + 545853 z^3 + 6492316 z^4 + 14454528 z^5 + 12300288 z^6 + 3670016 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-29568 + 112112 z - 428967 z^2 + 2513973 z^3 + 69637504 z^4 + 188135424 z^5 + 180289536 z^6 + 58720256 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (93364366095 Pi z^4 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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<apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 93364366095 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02