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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.bjm5.01

 Input Form

 Hypergeometric2F1[-(25/8), 6, 15/8, -z] == (1/68719476736) (1785 (262144/(1 + z) + (1/z^(7/8)) (42075 (-1)^(1/8) (Log[1 - (-1)^(1/8) z^(1/8)] - Log[1 + (-1)^(1/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(3/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(3/8) z^(1/8)] + I Log[1 - (-1)^(5/8) z^(1/8)] - I Log[1 + (-1)^(5/8) z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(7/8) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(7/8) z^(1/8)])) + (18784150/3) (-8 + 72 z + 9 (-1)^(1/8) z^(9/8) Log[1 - (-1)^(1/8) z^(1/8)] - 9 (-1)^(1/8) z^(9/8) Log[1 + (-1)^(1/8) z^(1/8)] + 9 (-1)^(3/8) z^(9/8) Log[1 - (-1)^(3/8) z^(1/8)] - 9 (-1)^(3/8) z^(9/8) Log[1 + (-1)^(3/8) z^(1/8)] + 9 (-1)^(5/8) z^(9/8) Log[1 - (-1)^(5/8) z^(1/8)] - 9 (-1)^(5/8) z^(9/8) Log[1 + (-1)^(5/8) z^(1/8)] + 9 (-1)^(7/8) z^(9/8) Log[1 - (-1)^(7/8) z^(1/8)] - 9 (-1)^(7/8) z^(9/8) Log[1 + (-1)^(7/8) z^(1/8)]) + 81876795 (8 (-(1/25) + z/17 - z^2/9 + z^3) + (-1)^(1/8) z^(25/8) (Log[1 - (-1)^(1/8) z^(1/8)] - Log[1 + (-1)^(1/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(3/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(3/8) z^(1/8)] + I Log[1 - (-1)^(5/8) z^(1/8)] - I Log[1 + (-1)^(5/8) z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(7/8) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(7/8) z^(1/8)])) - 6900300 (-8 + (-1)^(1/8) z^(1/8) (-Log[1 - (-1)^(1/8) z^(1/8)] + Log[1 + (-1)^(1/8) z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(3/8) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(3/8) z^(1/8)] - I Log[1 - (-1)^(5/8) z^(1/8)] + I Log[1 + (-1)^(5/8) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(7/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(7/8) z^(1/8)])) - 125964300 (-(8/17) + (8 z)/9 - 8 z^2 + (-1)^(1/8) z^(17/8) (-Log[1 - (-1)^(1/8) z^(1/8)] + Log[1 + (-1)^(1/8) z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(3/8) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(3/8) z^(1/8)] - I Log[1 - (-1)^(5/8) z^(1/8)] + I Log[1 + (-1)^(5/8) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(7/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(7/8) z^(1/8)]))))

 Standard Form

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 MathML Form

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

 2007-05-02