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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=4, b>=a > For fixed z and a=4, b=5





http://functions.wolfram.com/07.23.03.amz9.01









  


  










Input Form





Hypergeometric2F1[4, 5, -(21/4), z] == (1/29198647296) ((1/(-1 + z)^14) (8 (3649830912 - 65001750528 z + 575865618432 z^2 - 3492233084928 z^3 + 17455089713152 z^4 - 91891758006272 z^5 + 1405857011335168 z^6 + 3436310869067783 z^7 + 1638006102181268 z^8 + 158353102309088 z^9 + 525866140800 z^10)) - (1/(1 - z)^(57/4)) (336882996450 Sqrt[2] z^(25/4) (11803 + 19536 z + 7104 z^2 + 512 z^3) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/(1 - z)^(57/4)) (336882996450 Sqrt[2] z^(25/4) (11803 + 19536 z + 7104 z^2 + 512 z^3) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) + (1/(1 - z)^(57/4)) (168441498225 Sqrt[2] z^(25/4) (11803 + 19536 z + 7104 z^2 + 512 z^3) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) - (1/(1 - z)^(57/4)) (168441498225 Sqrt[2] z^(25/4) (11803 + 19536 z + 7104 z^2 + 512 z^3) 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