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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=-9/4, b>=a > For fixed z and a=-9/4, b=23/4





http://functions.wolfram.com/07.23.03.aep0.01









  


  








Input Form





Hypergeometric2F1[-(9/4), 23/4, -(9/2), z] == (1/(3932544 Pi^(3/2))) (((1/(-1 + z)^8) (4 (491568 - 2457840 z + 3878413 z^2 - 766612 z^3 - 1003618 z^4 - 4628932 z^5 + 18383885 z^6 - 25031584 z^7 + 17344256 z^8 - 6209536 z^9 + 917504 z^10) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^8) (4 (491568 - 2457840 z + 3878413 z^2 - 766612 z^3 - 1003618 z^4 - 4628932 z^5 + 18383885 z^6 - 25031584 z^7 + 17344256 z^8 - 6209536 z^9 + 917504 z^10) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^7)) ((-983136 + 491568 Sqrt[z] + 4424112 z - 2007236 z^(3/2) - 5749590 z^2 + 2055515 z^(5/2) - 522291 z^3 + 1054823 z^(7/2) + 952413 z^4 + 10241 z^(9/2) + 9247623 z^5 - 15960559 z^(11/2) - 20807211 z^6 + 31310528 z^(13/2) + 18752640 z^7 - 26621440 z^(15/2) - 8067072 z^8 + 11042816 z^(17/2) + 1376256 z^9 - 1835008 z^(19/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^8)) ((983136 + 491568 Sqrt[z] - 4424112 z - 2007236 z^(3/2) + 5749590 z^2 + 2055515 z^(5/2) + 522291 z^3 + 1054823 z^(7/2) - 952413 z^4 + 10241 z^(9/2) - 9247623 z^5 - 15960559 z^(11/2) + 20807211 z^6 + 31310528 z^(13/2) - 18752640 z^7 - 26621440 z^(15/2) + 8067072 z^8 + 11042816 z^(17/2) - 1376256 z^9 - 1835008 z^(19/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^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