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Omega Constant

المؤلف:  Michon, G. P.

المصدر:  "Final Answers: Numerical Constants." http://home.att.net/~numericana/answer/constants.htm#mertens.

الجزء والصفحة:  ...

22-7-2019

2283

Omega Constant

 

The omega constant is defined as

(1)

(OEIS A030178), where  is the Lambert W-function. It is available in the Wolfram Language using the function ProductLog[1].  can be considered a sort of "golden ratio" for exponentials since

(2)

giving

(3)

The omega constant is also given by the power tower

(4)

where .

A beautiful integral involving  given by

			(5)
			(6)

is due to V. Adamchik (OEIS A115287; Moll 2006; typo corrected).

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REFERENCES:

Michon, G. P. "Final Answers: Numerical Constants." http://home.att.net/~numericana/answer/constants.htm#mertens.

Moll, V. H. "Some Questions in the Evaluation of Definite Integrals." MAA Short Course, San Antonio, TX. Jan. 2006. http://crd.lbl.gov/~dhbailey/expmath/maa-course/Moll-MAA.pdf.

Sloane, N. J. A. Sequences A030178 and A115287 in "The On-Line Encyclopedia of Integer Sequences."