OFFSET
1,1
COMMENTS
The coefficient a for which y=a*sqrt(x) kisses the exponential function y=exp(x). The kissing point is (0.5, sqrt(e)). For more details, see A257776. Also, inverse of this constant equals the maximum value of sqrt(x)*exp(-x) for positive x, attained at x=1/2. - Stanislav Sykora, Nov 04 2015
LINKS
Ivan Panchenko, Table of n, a(n) for n = 1..1000
FORMULA
From Amiram Eldar, Jul 08 2023: (Start)
Equals Product_{n>=0} (e / (1 + 1/(n-1/2))^n).
Equals Product_{n>=0} (e * (1 - 1/(n+1/2))^n). (End)
EXAMPLE
2.3316439815971242033635360621684008763802362991875884230...
MATHEMATICA
RealDigits[Sqrt[2*E], 10, 100][[1]] (* G. C. Greubel, Sep 08 2018 *)
PROG
(PARI) sqrt(2*exp(1)) \\ Michel Marcus, Nov 05 2015
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(2*Exp(1)); // G. C. Greubel, Sep 08 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved