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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 4 and fixed z > For fixed z and a=2, b>=a > For fixed z and a=2, b=5





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









  


  








Input Form





Hypergeometric2F1[2, 5, -(3/4), z] == (1/196608) ((8 (-24576 + 499712 z + 3434539 z^2 + 729036 z^3 - 105952 z^4 + 9856 z^5))/(-1 + z)^7 + (1009470 Sqrt[2] z^(7/4) (11 + 16 z) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(31/4) + (1009470 Sqrt[2] z^(7/4) (11 + 16 z) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(31/4) + (504735 Sqrt[2] z^(7/4) (11 + 16 z) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(31/4) - (504735 Sqrt[2] z^(7/4) (11 + 16 z) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(31/4))








Standard Form





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MathML Form







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<plus /> <apply> <times /> <cn type='integer'> 9856 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 105952 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 729036 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3434539 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 499712 </cn> <ci> z </ci> </apply> <cn type='integer'> -24576 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 7 </cn> </apply> <cn type='integer'> -1 </cn> </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