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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=-23/4, b>=a > For fixed z and a=-23/4, b=-23/4





http://functions.wolfram.com/07.23.03.8949.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(23/4), 2, -z] == (8 Sqrt[2] ((-Sqrt[1 + z]) (168245 - 37188846 z + 397114911 z^2 - 1006696724 z^3 + 763276707 z^4 - 164947230 z^5 + 6799337 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (168245 - 37020601 z + 359926065 z^2 - 609581813 z^3 - 243420017 z^4 + 598329477 z^5 - 158147893 z^6 + 6799337 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (168245 - 37188846 z + 397114911 z^2 - 1006696724 z^3 + 763276707 z^4 - 164947230 z^5 + 6799337 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (168245 - 6400011 z - 135764091 z^2 + 1167575101 z^3 - 2124746841 z^4 + 1151997111 z^5 - 174326497 z^6 + 4542615 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (122650605 Pi z Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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-1 </cn> <apply> <times /> <cn type='integer'> 135764091 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6400011 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 168245 </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