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Takeuchi-Prellberg Constant

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Prellberg (2001) noted that the limit

c=lim_(n->infty)(T_n)/(B_nexp{1/2[W(n)]^2})=2.2394331040...

(OEIS A143307) exists, where T_n is a Takeuchi number, B_n is a Bell number, and W(n) is the Lambert W-function (Finch 2003, p. 321).

See also

TAK Function, Takeuchi Number

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References

Finch, S. R. "Takeuchi-Prellberg Constant." §5.8 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 321-322, 2003.Prellberg, T. "On the Asymptotics of Takeuchi Numbers." In Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics. Dordrecht, Netherlands: Kluwer, pp. 231-242, 2001.Sloane, N. J. A. Sequence A143307 in "The On-Line Encyclopedia of Integer Sequences."

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Takeuchi-Prellberg Constant

Cite this as:

Weisstein, Eric W. "Takeuchi-Prellberg Constant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Takeuchi-PrellbergConstant.html

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