OFFSET
0,1
COMMENTS
The function f(x)=log(x)*log(1+x) is zero at x=0 and zero at x=1, and attains a local minimum at x=0.318...
This constant equals the zero of the first derivative, i.e., it satisfies (1+x)*log(1+x) + x*log(x) = 0.
EXAMPLE
Equals 0.3183657369410991840261143... The ordinate value is -0.31634671137020605439495...
MAPLE
Digits := 100 ; fsolve( (1+x)*log(1+x)+x*log(x)) ;
MATHEMATICA
RealDigits[x /. FindRoot[(1 + x)*Log[1 + x] + x*Log[x], {x, 1}, WorkingPrecision -> 120], 10, 100][[1]] (* Amiram Eldar, Jun 23 2021 *)
PROG
(PARI) solve(x=0.3, 0.4, x*log(x)+(1+x)*log(1+x)) \\ M. F. Hasler, Jun 23 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Jun 21 2021
STATUS
approved