OFFSET
1,1
COMMENTS
Conjecture: (phi^phi - 1/phi)/2 = integral_{x=0..oo} exp(-x*(2 + phi)) * (cosh(x) + sqrt(5) * sinh(x))^phi dx.
LINKS
Alexander R. Povolotsky, Interesting Integral, post in newsgroup sci.math.research, April 04, 2017.
EXAMPLE
0.78021178959385214958397943425280386704336706094374587460616665067108999335696...
MATHEMATICA
RealDigits[(GoldenRatio^GoldenRatio - 1/GoldenRatio)/2, 10, 120][[1]]
PROG
(Magma) (((Sqrt(5)+1)/2)^((Sqrt(5)+1)/2) - 1/((Sqrt(5)+1)/2))/2
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vincenzo Librandi, Dec 29 2019
STATUS
approved