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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=-3/2





http://functions.wolfram.com/07.23.03.ae2z.01









  


  








Input Form





Hypergeometric2F1[-(9/4), -(3/2), 6, z] == (128 Sqrt[2] (2 (24576 - 286464 z + 1624048 z^2 - 6340240 z^3 + 23559900 z^4 + 224834402 z^5 + 83628727 z^6 + 1537536 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (24576 - 286464 z + 1624048 z^2 - 6340240 z^3 + 23559900 z^4 + 224834402 z^5 + 83628727 z^6 + 1537536 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (24576 - 274176 z + 1490800 z^2 - 5635760 z^3 + 20954700 z^4 + 76656242 z^5 + 16311113 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (24576 - 286464 z + 1624048 z^2 - 6340240 z^3 + 23559900 z^4 + 224834402 z^5 + 83628727 z^6 + 1537536 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (24576 - 286464 z + 1624048 z^2 - 6340240 z^3 + 23559900 z^4 + 224834402 z^5 + 83628727 z^6 + 1537536 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (24576 - 286464 z + 1624048 z^2 - 6340240 z^3 + 23559900 z^4 + 224834402 z^5 + 83628727 z^6 + 1537536 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (10104269175 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