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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=-15/4





http://functions.wolfram.com/07.23.03.ab10.01









  


  










Input Form





Hypergeometric2F1[-(15/4), -(15/4), 3, -z] == (64 Sqrt[2] (-2 Sqrt[1 + z] (770 + 25025 z - 1039328 z^2 + 2773022 z^3 - 1423402 z^4 + 114713 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - 2 (770 + 25795 z - 1014303 z^2 + 1733694 z^3 + 1349620 z^4 - 1308689 z^5 + 114713 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 Sqrt[1 + z] (770 + 25025 z - 1039328 z^2 + 2773022 z^3 - 1423402 z^4 + 114713 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (1540 + 51205 z + 256369 z^2 - 6642798 z^3 + 10921222 z^4 - 3559911 z^5 + 168245 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (73523065 Pi z^2 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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<times /> <cn type='integer'> 51205 </cn> <ci> z </ci> </apply> <cn type='integer'> 1540 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <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> <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> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02