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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=-3/8, b>=a > For fixed z and a=-3/8, b=7/8





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









  


  










Input Form





Hypergeometric2F1[-(3/8), 7/8, 6, z] == (1/(23822065575 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (32768 - 180096 z + 405955 z^2 - 478269 z^3 + 313137 z^4 + 14025 z^5) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-4096 + 19536 z - 36839 z^2 + 34254 z^3 + 14025 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 10 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-2048 + 10920 z - 23683 z^2 + 26499 z^3 - 25245 z^4 + 2805 z^5) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (32768 - 180096 z + 405955 z^2 - 478269 z^3 + 313137 z^4 + 14025 z^5) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))










Standard Form





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MathML Form







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</cn> <apply> <times /> <cn type='integer'> 180096 </cn> <ci> z </ci> </apply> </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> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02