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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=-7/2, b>=a > For fixed z and a=-7/2, b=-7/4





http://functions.wolfram.com/07.23.03.aby8.01









  


  








Input Form





Hypergeometric2F1[-(7/2), -(7/4), 4, z] == (2 Sqrt[2] (-2 (1 - z)^(1/4) (-3584 + 53984 z - 550704 z^2 - 8259304 z^3 - 6720824 z^4 - 395010 z^5 + 13167 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (-3584 + 53984 z - 550704 z^2 - 8259304 z^3 - 6720824 z^4 - 395010 z^5 + 13167 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-3584 + 55776 z - 577360 z^2 + 1425560 z^3 + 10697040 z^4 + 4260454 z^5 + 4389 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-3584 + 53984 z - 550704 z^2 - 8259304 z^3 - 6720824 z^4 - 395010 z^5 + 13167 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-3584 + 53984 z - 550704 z^2 - 8259304 z^3 - 6720824 z^4 - 395010 z^5 + 13167 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-3584 + 53984 z - 550704 z^2 - 8259304 z^3 - 6720824 z^4 - 395010 z^5 + 13167 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (9414405 Pi Sqrt[1 + Sqrt[1 - z]] z^3)








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