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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=-3/4





http://functions.wolfram.com/07.23.03.a9aj.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(3/4), 11/2, z] == (1/(43235274225 Pi^(3/2) z^(9/2))) (32 (2 (-351120 + 4827900 z - 33577313 z^2 + 174914817 z^3 - 1237435914 z^4 - 2773032130 z^5 - 186617925 z^6 + 28166229 z^7 - 3680976 z^8 + 254592 z^9) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (-351120 + 4827900 z - 33577313 z^2 + 174914817 z^3 - 1237435914 z^4 - 2773032130 z^5 - 186617925 z^6 + 28166229 z^7 - 3680976 z^8 + 254592 z^9) EllipticE[(1/2) (1 + Sqrt[z])] - (-351120 - 175560 Sqrt[z] + 4827900 z + 2399320 z^(3/2) - 33577313 z^2 - 16594809 z^(5/2) + 174914817 z^3 + 86154189 z^(7/2) - 1237435914 z^4 - 1963169890 z^(9/2) - 2773032130 z^5 - 2141098830 z^(11/2) - 186617925 z^6 + 6792435 z^(13/2) + 28166229 z^7 - 902343 z^(15/2) - 3680976 z^8 + 63648 z^(17/2) + 254592 z^9) EllipticK[(1/2) (1 - Sqrt[z])] + (-351120 + 175560 Sqrt[z] + 4827900 z - 2399320 z^(3/2) - 33577313 z^2 + 16594809 z^(5/2) + 174914817 z^3 - 86154189 z^(7/2) - 1237435914 z^4 + 1963169890 z^(9/2) - 2773032130 z^5 + 2141098830 z^(11/2) - 186617925 z^6 - 6792435 z^(13/2) + 28166229 z^7 + 902343 z^(15/2) - 3680976 z^8 - 63648 z^(17/2) + 254592 z^9) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02