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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=-1/4, b>=a > For fixed z and a=-1/4, b=-1/4





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









  


  








Input Form





Hypergeometric2F1[-(1/4), -(1/4), 6, -z] == (16384 Sqrt[2] ((-2048 - 13984 z - 41651 z^2 - 72449 z^3 - 90841 z^4 + 173653 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (-2048 - 13984 z - 41651 z^2 - 72449 z^3 - 90841 z^4 + 173653 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-2048 - 13472 z - 38523 z^2 - 64247 z^3 - 78413 z^4 + 69615 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-2048 - 13984 z - 41651 z^2 - 72449 z^3 - 90841 z^4 + 173653 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (969249645 Pi z^5 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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<apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </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> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02