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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.by9b.01

 Input Form

 Hypergeometric2F1[1/8, 6, 41/8, -z] == -((2805 (-1)^(1/8) (-214200 (-1)^(7/8) z^(1/8) + 323680 (-1)^(7/8) z^(9/8) - 575120 (-1)^(7/8) z^(17/8) + 1437408 (-1)^(7/8) z^(25/8) + 3336840 (-1)^(7/8) z^(33/8) - 105 (-1)^(3/4) (255 - 357 z + 630 z^2 - 1610 z^3 + 24955 z^4 + 27807 z^5) Log[1 - (-1)^(1/8) z^(1/8)] + 105 (-1)^(3/4) (255 - 357 z + 630 z^2 - 1610 z^3 + 24955 z^4 + 27807 z^5) Log[1 + (-1)^(1/8) z^(1/8)] - 26775 I Log[1 - (-1)^(3/8) z^(1/8)] + 37485 I z Log[1 - (-1)^(3/8) z^(1/8)] - 66150 I z^2 Log[1 - (-1)^(3/8) z^(1/8)] + 169050 I z^3 Log[1 - (-1)^(3/8) z^(1/8)] - 2620275 I z^4 Log[1 - (-1)^(3/8) z^(1/8)] - 2919735 I z^5 Log[1 - (-1)^(3/8) z^(1/8)] + 26775 I Log[1 + (-1)^(3/8) z^(1/8)] - 37485 I z Log[1 + (-1)^(3/8) z^(1/8)] + 66150 I z^2 Log[1 + (-1)^(3/8) z^(1/8)] - 169050 I z^3 Log[1 + (-1)^(3/8) z^(1/8)] + 2620275 I z^4 Log[1 + (-1)^(3/8) z^(1/8)] + 2919735 I z^5 Log[1 + (-1)^(3/8) z^(1/8)] - 26775 (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] + 37485 (-1)^(1/4) z Log[1 - (-1)^(5/8) z^(1/8)] - 66150 (-1)^(1/4) z^2 Log[1 - (-1)^(5/8) z^(1/8)] + 169050 (-1)^(1/4) z^3 Log[1 - (-1)^(5/8) z^(1/8)] - 2620275 (-1)^(1/4) z^4 Log[1 - (-1)^(5/8) z^(1/8)] - 2919735 (-1)^(1/4) z^5 Log[1 - (-1)^(5/8) z^(1/8)] + 26775 (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] - 37485 (-1)^(1/4) z Log[1 + (-1)^(5/8) z^(1/8)] + 66150 (-1)^(1/4) z^2 Log[1 + (-1)^(5/8) z^(1/8)] - 169050 (-1)^(1/4) z^3 Log[1 + (-1)^(5/8) z^(1/8)] + 2620275 (-1)^(1/4) z^4 Log[1 + (-1)^(5/8) z^(1/8)] + 2919735 (-1)^(1/4) z^5 Log[1 + (-1)^(5/8) z^(1/8)] - 26775 Log[1 - (-1)^(7/8) z^(1/8)] + 37485 z Log[1 - (-1)^(7/8) z^(1/8)] - 66150 z^2 Log[1 - (-1)^(7/8) z^(1/8)] + 169050 z^3 Log[1 - (-1)^(7/8) z^(1/8)] - 2620275 z^4 Log[1 - (-1)^(7/8) z^(1/8)] - 2919735 z^5 Log[1 - (-1)^(7/8) z^(1/8)] + 26775 Log[1 + (-1)^(7/8) z^(1/8)] - 37485 z Log[1 + (-1)^(7/8) z^(1/8)] + 66150 z^2 Log[1 + (-1)^(7/8) z^(1/8)] - 169050 z^3 Log[1 + (-1)^(7/8) z^(1/8)] + 2620275 z^4 Log[1 + (-1)^(7/8) z^(1/8)] + 2919735 z^5 Log[1 + (-1)^(7/8) z^(1/8)]))/(68719476736 z^(33/8) (1 + z)))

 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