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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=-19/4, b>=a > For fixed z and a=-19/4, b=11/2





http://functions.wolfram.com/07.23.03.a9vp.01









  


  








Input Form





Hypergeometric2F1[-(19/4), 11/2, 4, z] == (8 Sqrt[2] (2 (1 - z)^(1/4) (-26752 - 269192 z - 3165096 z^2 + 117254050 z^3 - 522830155 z^4 + 903957405 z^5 - 690537705 z^6 + 195634725 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + 2 (1 - z)^(3/4) (-26752 - 269192 z - 3165096 z^2 + 117254050 z^3 - 522830155 z^4 + 903957405 z^5 - 690537705 z^6 + 195634725 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - (1 - z)^(1/4) (-26752 - 269192 z - 3165096 z^2 + 117254050 z^3 - 522830155 z^4 + 903957405 z^5 - 690537705 z^6 + 195634725 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - Sqrt[1 - z] (-26752 - 269192 z - 3165096 z^2 + 117254050 z^3 - 522830155 z^4 + 903957405 z^5 - 690537705 z^6 + 195634725 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - (1 - z)^(3/4) (-26752 - 269192 z - 3165096 z^2 + 117254050 z^3 - 522830155 z^4 + 903957405 z^5 - 690537705 z^6 + 195634725 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - (-26752 - 255816 z - 3027992 z^2 + 13247290 z^3 + 121858125 z^4 - 608545600 z^5 + 1010763390 z^6 - 729664650 z^7 + 195634725 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)]))/(422463195 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