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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=-15/4, b>=a > For fixed z and a=-15/4, b=21/4





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









  


  










Input Form





Hypergeometric2F1[-(15/4), 21/4, 5/2, z] == (1/(2197845 Pi^(3/2) z^(3/2))) (4 (2 (5082 + 200739 z - 3739520 z^2 + 14223360 z^3 - 19070976 z^4 + 8388608 z^5) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (5082 + 200739 z - 3739520 z^2 + 14223360 z^3 - 19070976 z^4 + 8388608 z^5) EllipticE[(1/2) (1 + Sqrt[z])] - (5082 + 2541 Sqrt[z] + 200739 z - 448880 z^(3/2) - 3739520 z^2 + 2534400 z^(5/2) + 14223360 z^3 - 4177920 z^(7/2) - 19070976 z^4 + 2097152 z^(9/2) + 8388608 z^5) EllipticK[(1/2) (1 - Sqrt[z])] + (5082 - 2541 Sqrt[z] + 200739 z + 448880 z^(3/2) - 3739520 z^2 - 2534400 z^(5/2) + 14223360 z^3 + 4177920 z^(7/2) - 19070976 z^4 - 2097152 z^(9/2) + 8388608 z^5) 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