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Knuth's Series

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Knuth's series is given by

S=sum_(k=1)^(infty)((k^k)/(k!e^k)-1/(sqrt(2pik)))
(1)
=-2/3-1/(sqrt(2pi))zeta(1/2)
(2)
=-0.08406950872765599646...
(3)

(OEIS A096616), where zeta(z) is the Riemann zeta function (Knuth 2000; Borwein et al. 2004, pp. 15-17).

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References

Bailey, D. H.; Borwein, J. M.; Calkin, N. J.; Girgensohn, R.; Luke, D. R.; and Moll, V. H. Experimental Mathematics in Action. Wellesley, MA: A K Peters, pp. 16 and 221, 2007.Borwein, J.; Bailey, D.; and Girgensohn, R. "Knuth's Series Problem." §1.5 in Experimentation in Mathematics: Computational Paths to Discovery. Wellesley, MA: A K Peters, pp. 15-17, 2004.Knuth, D. E. "Problem 10832." Amer. Math. Monthly 107, 863, 2000.Sloane, N. J. A. Sequence A096616 in "The On-Line Encyclopedia of Integer Sequences."

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Knuth's Series

Cite this as:

Weisstein, Eric W. "Knuth's Series." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KnuthsSeries.html

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