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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=35/8, b>=a > For fixed z and a=35/8, b=39/8





http://functions.wolfram.com/07.23.03.ccl0.01









  


  








Input Form





Hypergeometric2F1[35/8, 39/8, 4, z] == (2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (896 - 5565 z + 18270 z^2 + 39439 z^3) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - (896 (1 + Sqrt[1 - z] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) - 21 (281 + 265 Sqrt[1 - z] + 265 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z + 105 (193 + 174 Sqrt[1 - z] + 174 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 + (-104411 + 39439 Sqrt[1 - z] + 39439 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^3 - 16929 z^4) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (140821065 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(21/4) z^3)








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> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 21 <sep /> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </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