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Lambert transform

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The integral transform

The Lambert transform is the continuous analogue of the Lambert series (under the correspondence , ). The following inversion formula holds: Suppose that

and that

If also and if the function is continuous at , then one has

where is the Möbius function.

References

[1] D.V. Widder, "An inversion of the Lambert transform" Math. Mag. , 23 (1950) pp. 171–182
[2] V.A. Ditkin, A.P. Prudnikov, "Integral transforms" Progress in Math. , 4 (1969) pp. 1–85 Itogi Nauk. Mat. Anal. 1966 (1967) pp. 7–82
How to Cite This Entry:
Lambert transform. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lambert_transform&oldid=42007
This article was adapted from an original article by Yu.A. BrychkovA.P. Prudnikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article