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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=-23/4, b>=a > For fixed z and a=-23/4, b=-11/4





http://functions.wolfram.com/07.23.03.9215.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(11/4), 11/2, z] == (32 (-2 (11306064 - 238638708 z + 2746330433 z^2 - 26383339675 z^3 + 408411540845 z^4 + 3028808709193 z^5 + 3646247754259 z^6 + 967359821791 z^7 + 13824309135 z^8 - 630549465 z^9 + 21534240 z^10) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (11306064 - 238638708 z + 2746330433 z^2 - 26383339675 z^3 + 408411540845 z^4 + 3028808709193 z^5 + 3646247754259 z^6 + 967359821791 z^7 + 13824309135 z^8 - 630549465 z^9 + 21534240 z^10) EllipticE[(1/2) (1 + Sqrt[z])] + (11306064 + 5653032 Sqrt[z] - 238638708 z - 118848268 z^(3/2) + 2746330433 z^2 + 1363457480 z^(5/2) - 26383339675 z^3 - 13082058220 z^(7/2) + 408411540845 z^4 + 933369955600 z^(9/2) + 3028808709193 z^5 + 3538982527684 z^(11/2) + 3646247754259 z^6 + 3001326466024 z^(13/2) + 967359821791 z^7 + 578482364460 z^(15/2) + 13824309135 z^8 - 156123240 z^(17/2) - 630549465 z^9 + 5383560 z^(19/2) + 21534240 z^10) EllipticK[(1/2) (1 - Sqrt[z])] - (11306064 - 5653032 Sqrt[z] - 238638708 z + 118848268 z^(3/2) + 2746330433 z^2 - 1363457480 z^(5/2) - 26383339675 z^3 + 13082058220 z^(7/2) + 408411540845 z^4 - 933369955600 z^(9/2) + 3028808709193 z^5 - 3538982527684 z^(11/2) + 3646247754259 z^6 - 3001326466024 z^(13/2) + 967359821791 z^7 - 578482364460 z^(15/2) + 13824309135 z^8 + 156123240 z^(17/2) - 630549465 z^9 - 5383560 z^(19/2) + 21534240 z^10) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)/ (23366700478875 Pi^(3/2) z^(9/2))










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