TOPICS
Search

Takeuchi-Prellberg Constant

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook

The Takeuchi-Prellberg constant is defined by the conjectured limit (Prellberg 2001, pp. 236-237)

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

where T_n is a Takeuchi number, B_n is a Bell number, and W(n) is the real principal branch of the Lambert W-function. Prellberg (2001, p. 235) reported the numerical estimate c=2.2394331040... (OEIS A143307).

See also

TAK Function, Takeuchi Number

Explore with Wolfram|Alpha

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 (Ed. F. G. Garvan and M. E. H. Ismail). Dordrecht, Netherlands: Kluwer, pp. 231-242, 2001. https://doi.org/10.1007/978-1-4613-0257-5_14.Sloane, N. J. A. Sequence A143307 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Takeuchi-Prellberg Constant

Cite this as:

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

Subject classifications