OFFSET
0,3
LINKS
V. N. Nolte, Some probabilistic results on the convergents of continued fractions, Indagationes Mathematicae, Vol. 1, No. 3 (1990), pp. 381-389.
FORMULA
Equals Sum_{j >= 1} log_2(Gamma(1+1/(4*j+2))/Gamma(1+(j+1)/(2*j+1))*Gamma(1+(2*j+1)/4/j)/Gamma(1+1/4/j))).
EXAMPLE
0.1169400035780680765605607509208534105...
PROG
(PARI)
sumpos(j=1, log(gamma(1+1/(4*j+2))/gamma(1+(j+1)/(2*j+1))*gamma(1+(2*j+1)/4/j)/gamma(1+1/4/j)))/log(2)
(PARI)
C = log(2)-1+(log(72*Pi)-4*log(gamma(1/4)))/log(2)
C+sumpos(n=2, (-1)^n*(zeta(n)-1)/n*((2^(2-n)-2^(2-2*n)-1)*(zeta(n)-1)+(2^(n-1)-1)*2^(2-2*n)))/log(2)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
A.H.M. Smeets, Feb 16 2021
STATUS
approved