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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=2





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









  


  








Input Form





Hypergeometric2F1[1, 2, -(19/4), z] == (-29260 + 217140 z - 710556 z^2 + 1366148 z^3 - 1803588 z^4 + 2306076 z^5 + 168245 z^6)/(29260 (-1 + z)^7) + (621 z^(23/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(8 Sqrt[2] (1 - z)^(31/4)) + (621 z^(23/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(8 Sqrt[2] (1 - z)^(31/4)) + (621 z^(23/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(16 Sqrt[2] (1 - z)^(31/4)) - (621 z^(23/4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(16 Sqrt[2] (1 - z)^(31/4))








Standard Form





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MathML Form







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</cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 29260 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 7 </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