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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=-15/4





http://functions.wolfram.com/07.23.03.9117.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(15/4), 5/2, z] == (1/(2230812675 Pi^(3/2) z^(3/2))) (4 (4 (1110417 - 84391692 z - 2116409477 z^2 - 7544875590 z^3 - 6628154265 z^4 - 1331614096 z^5 - 12711699 z^6 + 306306 z^7) EllipticE[(1/2) (1 - Sqrt[z])] - 4 (1110417 - 84391692 z - 2116409477 z^2 - 7544875590 z^3 - 6628154265 z^4 - 1331614096 z^5 - 12711699 z^6 + 306306 z^7) EllipticE[(1/2) (1 + Sqrt[z])] - (2220834 + 1110417 Sqrt[z] - 168783384 z - 642002326 z^(3/2) - 4232818954 z^2 - 6863872785 z^(5/2) - 15089751180 z^3 - 16072018740 z^(7/2) - 13256308530 z^4 - 10334202785 z^(9/2) - 2663228192 z^5 - 1522647126 z^(11/2) - 25423398 z^6 + 153153 z^(13/2) + 612612 z^7) EllipticK[(1/2) (1 - Sqrt[z])] + (2220834 - 1110417 Sqrt[z] - 168783384 z + 642002326 z^(3/2) - 4232818954 z^2 + 6863872785 z^(5/2) - 15089751180 z^3 + 16072018740 z^(7/2) - 13256308530 z^4 + 10334202785 z^(9/2) - 2663228192 z^5 + 1522647126 z^(11/2) - 25423398 z^6 - 153153 z^(13/2) + 612612 z^7) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^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