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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=2





http://functions.wolfram.com/07.23.03.akt8.01









  


  








Input Form





Hypergeometric2F1[2, 2, -(9/4), z] == (1/5760) (-((8 (-720 + 5600 z - 23088 z^2 + 159552 z^3 + 67501 z^4))/ (-1 + z)^6) + (19890 Sqrt[2] z^(13/4) (17 + 4 z) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(25/4) + (19890 Sqrt[2] z^(13/4) (17 + 4 z) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(25/4) - (9945 Sqrt[2] z^(13/4) (17 + 4 z) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(25/4) + (9945 Sqrt[2] z^(13/4) (17 + 4 z) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(25/4))








Standard Form





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MathML Form







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<cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 159552 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 23088 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5600 </cn> <ci> z </ci> </apply> <cn type='integer'> -720 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 6 </cn> </apply> <cn type='integer'> -1 </cn> </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