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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=27/8, b>=a > For fixed z and a=27/8, b=39/8





http://functions.wolfram.com/07.23.03.cah5.01









  


  








Input Form





Hypergeometric2F1[27/8, 39/8, 1, z] == -((2 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (3974983 + 21424835 z + 11684501 z^2 + 43681 z^3) EllipticE[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-1240612 + 3974983 Sqrt[1 - z] + 3974983 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] + (-27658088 + 21424835 Sqrt[1 - z] + 21424835 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z + (-40290304 + 11684501 Sqrt[1 - z] + 11684501 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 + 43681 (-120 + Sqrt[1 - z] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^3 + 174724 z^4) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (5215595 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(29/4)))








Standard Form





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MathML Form







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type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 29 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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