Dirichlet Lambda Function

Min   Max       Re       Im

The Dirichlet lambda function  is the Dirichlet L-series defined by

			(1)
			(2)

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

			(5)
			(6)

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.