OFFSET
1,1
COMMENTS
This constant is irrational (Mingarelli, 2013).
LINKS
Angelo B. Mingarelli, Abstract factorials, Notes on Number Theory and Discrete Mathematics, Vol. 19, No. 4 (2013), pp. 43-76 (see p. 62); arXiv preprint, arXiv:0705.4299 [math.NT], 2007-2012.
Eric Weisstein's World of Mathematics, Bessel Function of the First Kind.
Eric Weisstein's World of Mathematics, Modified Bessel Function of the First Kind.
FORMULA
Equals (1/4)*(2+sqrt(2)) * BesselI(0,2^(5/4)) + (1/4)*(2-sqrt(2)) * BesselJ(0, 2^(5/4)), where BesselJ is the Bessel function of the first kind, and BesselI is the modified Bessel function of the first kind.
EXAMPLE
2.56279353478318946160768164513857133515084906789206...
MAPLE
evalf(sum(2^floor(k/2)/k!^2, k=0..infinity), 140); # Alois P. Heinz, Jul 03 2021
MATHEMATICA
RealDigits[(1/4) * (2+Sqrt[2]) * BesselI[0, 2^(5/4)] + (1/4) * (2-Sqrt[2]) * BesselJ[0, 2^(5/4)], 10, 100][[1]]
PROG
(PARI) suminf(k=0, 2^floor(k/2)/(k!^2)) \\ Michel Marcus, Jul 02 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jul 02 2021
STATUS
approved