OFFSET
1,2
COMMENTS
e^(1/4) is also the integral from 0 to infinity of e^(-x) * I_0(sqrt(x)), where I_0(z) is a modified Bessel function. - Jean-François Alcover, Mar 10 2011
e^(1/4) maximizes the value of x^(c/(x^4)) for any real positive constant c, and minimizes for it for a negative constant, on the range x > 0. - A.H.M. Smeets, Aug 16 2018
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
D. M. Bătinetu-Giurgiu, Problem 4133, Crux Mathematicorum, Vol. 42, No. 4 (2016), p. 174; Solution to Problem 4133, ibid., Vol. 43, No. 4 (2017), pp. 167-169.
FORMULA
e^(1/4) = 1/2*( 1 +(5 +(9 +(13 +...)/12)/8)/4 ) = 1 +(1 +(1 +(1 +...)/12)/8)/4. - Rok Cestnik, Jan 19 2017
Equals lim_{n->oo} ((2*n-1)!!)^(1/(2*n))/A057863(n)^(1/n^2) (Bătinetu-Giurgiu, 2016). - Amiram Eldar, Apr 10 2022
EXAMPLE
1.28402541668774148407342056806243645833....
MAPLE
evalf(exp(1/4)); # Muniru A Asiru, Aug 16 2018
MATHEMATICA
RealDigits[(E)^(1/4), 10, 100][[1]] (* Vincenzo Librandi, Mar 01 2013 *)
PROG
(PARI) exp(1/4) \\ Michel Marcus, Jan 19 2017
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Mohammad K. Azarian, Mar 27 2004
STATUS
approved