Dirichlet Lambda Function
المؤلف:
Abramowitz, M. and Stegun, I. A.
المصدر:
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
...
7-9-2019
1715
Dirichlet Lambda Function
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
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.
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