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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=17/8, b>=a > For fixed z and a=17/8, b=37/8





http://functions.wolfram.com/07.23.03.c6lf.01









  


  








Input Form





Hypergeometric2F1[17/8, 37/8, 6, z] == (524288 2^(1/4) ((1/(1 - z)^(3/4)) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (32768 - 30848 z + 387 z^2 + 108 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) - (1/(1 - z)^(3/4)) (Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (32768 - 30848 z + 387 z^2 + 108 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) - ((32768 - 30848 z + 387 z^2 + 108 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])/ Sqrt[1 - z] + (-32768 + 10368 z + 1773 z^2 + 432 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (57358665 Pi (1 + Sqrt[1 - z])^(1/4) z^5)








Standard Form





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MathML Form







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/> <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