Complex Polylogarithm Function


For Polylog(s, x) with s.i == 0 and x.i == 0 and x.r <= 1, use the real Polylog(s.r, x.r) function.

See: Real Polylogarithm Function

Else if s == 2 and x.r < −1, compute y = 1 / (1 − x), compute z = Polylog(2, 1−y), then

Polylog(a, x) = −z − (Ln(y))^2 / 2.

Else if x.r > 1 and s != 2, Error "Cannot always compute Polylog(s, x) for x > 1 and s != 2"

Else

Polylog(s, x) = x * Lerch(x, s, 1).

See: Polylogarithm -- From MathWorld
And: Wolfram Function Evaluation -- PolyLog

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This page accessed times since Feb 13, 2006.
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Changes last made on Monday, 06-Aug-07 16:15:43 PDT

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