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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 8 and fixed z and a>0 > For fixed z and a=5/8, b>=a > For fixed z and a=5/8, b=47/8





http://functions.wolfram.com/07.23.03.c0hs.01









  


  








Input Form





Hypergeometric2F1[5/8, 47/8, 6, z] == (1/(38444150745 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (32768 + 32896 z + 35139 z^2 + 40092 z^3 + 53040 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 10 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-2048 - 2392 z - 2691 z^2 - 3120 z^3 + 10608 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1/Sqrt[1 - z]) (3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (4096 + 2992 z + 2743 z^2 + 2964 z^3 + 53040 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) + 2 (32768 + 32896 z + 35139 z^2 + 40092 z^3 + 53040 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))








Standard Form





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MathML Form







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type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 32896 </cn> <ci> z </ci> </apply> <cn type='integer'> 32768 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </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> </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