Complex Dirichlet Lambda Function


The Dirichlet Lambda function Lam(x) = 1 + 3^−x + 5^−x + ... = Sum{k=1, infinity}[(2k−1)^−x], x > 1. Lambda is defined for all values of x except x = 1 where it is infinite.

For example, Lam(2) = 1 + 1/9 + 1/25 + 1/49 + ... = Pi^2/8 = 1.23370,05501,36169,82735... .

Lam(x) = 0 for x = 0 and all negative even integers.

For Lam(x) with x.i == 0, use the real Lam(x.r) function.

See: Real Dirichlet Lambda Function

Else

Lam(x) = Zeta(x) * (1 − 2^(−x))

See: Dirichlet Lambda Function -- From MathWorld
And: Wolfram Function Evaluation -- Zeta (Lam(x) = (1−2^(−x))*Zeta(x))

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Changes last made on Monday, 06-Aug-07 16:15:42 PDT

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