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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=13/4





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









  


  










Input Form





Hypergeometric2F1[-(15/4), 13/4, -(11/2), z] == (1/(31680 Pi^(3/2))) (((1/(-1 + z)^5) (2 Sqrt[z] (-15840 + 38160 z - 15582 z^2 - 7749 z^3 - 6300 z^4 - 7665 z^5 + 174720 z^6 - 202752 z^7 + 65536 z^8) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^5) (2 Sqrt[z] (-15840 + 38160 z - 15582 z^2 - 7749 z^3 - 6300 z^4 - 7665 z^5 + 174720 z^6 - 202752 z^7 + 65536 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^4)) ((-31680 + 47520 Sqrt[z] + 52560 z - 90720 z^(3/2) + 5880 z^2 + 9702 z^(5/2) - 8631 z^3 + 16380 z^(7/2) - 17010 z^4 + 23310 z^(9/2) - 27615 z^5 + 35280 z^(11/2) - 67200 z^6 - 107520 z^(13/2) + 153600 z^7 + 49152 z^(15/2) - 65536 z^8) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^5)) ((31680 + 47520 Sqrt[z] - 52560 z - 90720 z^(3/2) - 5880 z^2 + 9702 z^(5/2) + 8631 z^3 + 16380 z^(7/2) + 17010 z^4 + 23310 z^(9/2) + 27615 z^5 + 35280 z^(11/2) + 67200 z^6 - 107520 z^(13/2) - 153600 z^7 + 49152 z^(15/2) + 65536 z^8) 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