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    Dirichlet Lambda Function

    Definition

    The Dirichlet lambda function λ(x) is the Dirichlet L-series defined by λ(x) | congruent | sum_(n = 0)^∞ 1/(2n + 1)^x | = | (1 - 2^(-x)) ζ(x), where ζ(x) is the Riemann zeta function. The function is undefined at x = 1. It can be computed in closed form where ζ(x) can, that is for even positive n. The Dirichlet lambda function is implemented in the Wolfram Language as DirichletLambda[x].

    Related Wolfram Language symbol

    DirichletLambda

    Associated person

    Lejeune Dirichlet

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