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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=-11/2, b>=a > For fixed z and a=-11/2, b=21/4





http://functions.wolfram.com/07.23.03.a846.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 21/4, 4, z] == (-2 (1 - z)^(1/4) (157696 + 1567104 z + 18982656 z^2 - 1297589824 z^3 + 7503241056 z^4 - 17507733768 z^5 + 20153059080 z^6 - 11434670478 z^7 + 2562943383 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - 2 (1 - z)^(3/4) (157696 + 1567104 z + 18982656 z^2 - 1297589824 z^3 + 7503241056 z^4 - 17507733768 z^5 + 20153059080 z^6 - 11434670478 z^7 + 2562943383 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (157696 + 1488256 z + 18184320 z^2 - 630299200 z^3 + 3178927520 z^4 - 6813246024 z^5 + 7364799456 z^6 - 3974283390 z^7 + 854314461 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (157696 + 1567104 z + 18982656 z^2 - 1297589824 z^3 + 7503241056 z^4 - 17507733768 z^5 + 20153059080 z^6 - 11434670478 z^7 + 2562943383 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + Sqrt[1 - z] (157696 + 1567104 z + 18982656 z^2 - 1297589824 z^3 + 7503241056 z^4 - 17507733768 z^5 + 20153059080 z^6 - 11434670478 z^7 + 2562943383 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (157696 + 1567104 z + 18982656 z^2 - 1297589824 z^3 + 7503241056 z^4 - 17507733768 z^5 + 20153059080 z^6 - 11434670478 z^7 + 2562943383 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)])/(169234065 Sqrt[2] 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