dirichlet lambda function - Wolfram|Alpha

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Input interpretation

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].

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Related terms

Dirichlet beta function | Dirichlet eta function | Dirichlet L-series | Legendre's chi-function | Riemann zeta function | zeta function

Related Wolfram Language symbol

DirichletLambda

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