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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=5, b>=a > For fixed z and a=5, b=5





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









  


  










Input Form





Hypergeometric2F1[5, 5, -(5/4), z] == (1/33554432) (-((1/(-1 + z)^11) (8 (4194304 - 130023424 z + 7193231360 z^2 + 55302536645 z^3 + 78482622860 z^4 + 26123793056 z^5 + 1465143424 z^6))) - (1/(1 - z)^(45/4)) (696150 Sqrt[2] z^(9/4) (38675 + 190400 z + 201600 z^2 + 51200 z^3 + 2048 z^4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/(1 - z)^(45/4)) (696150 Sqrt[2] z^(9/4) (38675 + 190400 z + 201600 z^2 + 51200 z^3 + 2048 z^4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) + (1/(1 - z)^(45/4)) (348075 Sqrt[2] z^(9/4) (38675 + 190400 z + 201600 z^2 + 51200 z^3 + 2048 z^4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) - (1/(1 - z)^(45/4)) (348075 Sqrt[2] z^(9/4) (38675 + 190400 z + 201600 z^2 + 51200 z^3 + 2048 z^4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]))










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