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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=-7/8, b>=a > For fixed z and a=-7/8, b=35/8





http://functions.wolfram.com/07.23.03.btr4.01









  


  










Input Form





Hypergeometric2F1[-(7/8), 35/8, 5, z] == (65536 2^(1/4) (2 Sqrt[1 - z] (-7168 - 8288 z - 11193 z^2 - 20748 z^3 + 53040 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-7168 - 8288 z - 11193 z^2 - 20748 z^3 + 53040 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-7168 - 8288 z - 11193 z^2 - 20748 z^3 + 53040 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 (-3584 - 1904 z - 2639 z^2 - 6279 z^3 - 49920 z^4 + 53040 z^5) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (5492021535 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^4)










Standard Form





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MathML Form







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type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </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