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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=-9/4, b>=a > For fixed z and a=-9/4, b=-1/2





http://functions.wolfram.com/07.23.03.ae5i.01









  


  










Input Form





Hypergeometric2F1[-(9/4), -(1/2), 6, z] == (256 Sqrt[2] (-2 (-4096 + 40320 z - 186536 z^2 + 564480 z^3 - 1493550 z^4 - 7697617 z^5 - 640640 z^6 + 29568 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (-4096 + 40320 z - 186536 z^2 + 564480 z^3 - 1493550 z^4 - 7697617 z^5 - 640640 z^6 + 29568 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (4096 - 38272 z + 168040 z^2 - 486120 z^3 + 1273950 z^4 + 2197807 z^5 + 9856 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-4096 + 40320 z - 186536 z^2 + 564480 z^3 - 1493550 z^4 - 7697617 z^5 - 640640 z^6 + 29568 z^7) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (-4096 + 40320 z - 186536 z^2 + 564480 z^3 - 1493550 z^4 - 7697617 z^5 - 640640 z^6 + 29568 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (-4096 + 40320 z - 186536 z^2 + 564480 z^3 - 1493550 z^4 - 7697617 z^5 - 640640 z^6 + 29568 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (777251475 Pi Sqrt[1 + Sqrt[1 - z]] z^5)










Standard Form





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MathML Form







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Rule Form





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





2007-05-02