The Dirichlet lambda function is the Dirichlet
L-series defined by
where
is the Riemann zeta function. The function
is undefined at . It can be computed in closed form where can, that is for even positive .
The Dirichlet lambda function is implemented in the Wolfram
Language as DirichletLambda[x].
It is related to the Riemann zeta function
and Dirichlet eta function by
|
(3)
|
and
|
(4)
|
(Spanier and Oldham 1987). Special values of include
See also
Dirichlet Beta Function,
Dirichlet Eta Function,
Dirichlet
L-Series,
Legendre's Chi-Function,
Riemann Zeta Function,
Zeta
Function
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References
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, pp. 807-808, 1972.Spanier, J. and Oldham, K. B.
"The Zeta Numbers and Related Functions." Ch. 3 in An
Atlas of Functions. Washington, DC: Hemisphere, pp. 25-33, 1987.Referenced
on Wolfram|Alpha
Dirichlet Lambda Function
Cite this as:
Weisstein, Eric W. "Dirichlet Lambda Function."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DirichletLambdaFunction.html
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