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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=1, b>=a > For fixed z and a=1, b=6





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









  


  








Input Form





Hypergeometric2F1[1, 6, -(9/4), z] == (1/983040) ((1/(-1 + z)^9) (8 (-122880 + 1433600 z - 9207808 z^2 + 97353728 z^3 + 30080505 z^4 - 11565060 z^5 + 3787680 z^6 - 803712 z^7 + 79872 z^8)) + (222071850 Sqrt[2] z^(13/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(37/4) + (222071850 Sqrt[2] z^(13/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(37/4) - (111035925 Sqrt[2] z^(13/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(37/4) + (111035925 Sqrt[2] z^(13/4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(37/4))








Standard Form





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MathML Form







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/> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11565060 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 30080505 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 97353728 </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'> 9207808 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1433600 </cn> <ci> z </ci> </apply> <cn type='integer'> -122880 </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