There are a number of functions in mathematics commonly denoted with a Greek letter lambda. Examples of one-variable functions denoted with a lower case lambda include the Carmichael
functions , Dirichlet lambda function ,
elliptic lambda function , and Liouville
function . Examples of one-variable functions denoted with an upper case lambda include the Mangoldt
function and the lambda function defined by Jahnke and Emden (1945).
The triangle function , illustrated above, is commonly denoted .
The lambda function defined by Jahnke and Emden (1945) is
(1)
where
is a Bessel function of the first kind
and
is the gamma function . , and taking gives the special case
(2)
where
is the jinc function .
A two-variable lambda function is defined as
(3)
where
is the gamma function (McLachlan et al. 1950,
p. 9; Prudnikov et al. 1990, p. 798; Gradshteyn and Ryzhik 2000,
p. 1109).
See also Airy Functions ,
Carmichael Function ,
Dirichlet Lambda Function ,
Elliptic Lambda Function ,
Jinc
Function ,
Liouville Function ,
Mangoldt
Function ,
Mu Function ,
Nu
Function ,
Triangle Function
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References Gradshteyn, I. S. and Ryzhik, I. M. "The Functions ,
, , , ." §9.64 in Tables
of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press,
p. 1109, 2000. Jahnke, E. and Emde, F. Tables
of Functions with Formulae and Curves, 4th ed. New York: Dover, 1945. McLachlan,
N. W. et al. Supplément au formulaire pour le calcul symbolique.
Paris: L'Acad. des Sciences de Paris, Fasc. 113, p. 9, 1950. Prudnikov,
A. P.; Marichev, O. I.; and Brychkov, Yu. A. Integrals
and Series, Vol. 3: More Special Functions. Newark, NJ: Gordon and Breach,
1990. Referenced on Wolfram|Alpha Lambda Function
Cite this as:
Weisstein, Eric W. "Lambda Function."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/LambdaFunction.html
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