OFFSET
1,3
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.1, Shapiro-Drinfeld Constant, p. 209.
LINKS
V. G. Drinfel'd, A cyclic inequality, Mathematical Notes of the Academy of Sciences of the USSR, 9 (1971), 68-71.
Petros Hadjicostas, Plot of the curves y = exp(-x) and y = 2/(exp(x) + exp(x/2)) and their common tangent, 2020.
R. A. Rankin, 2743. An inequality, Mathematical Gazette, 42(339) (1958), 39-40.
B. A. Troesch, The validity of Shapiro's cyclic inequality, Mathematics of Computation, 53 (1989), 657-664.
Eric Weisstein's World of Mathematics, Shapiro's Cyclic Sum Constant.
FORMULA
EXAMPLE
1.1610777510328318186075949...
PROG
(PARI) c(b) = b + exp(b/2)/(2*exp(b)+exp(b/2));
y(b) = 2/(exp(b) + exp(b/2));
a=solve(b=-2, 2, exp(-c(b))*(1-b+c(b))-2/(exp(b)+exp(b/2)));
y(a)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Petros Hadjicostas, Jun 02 2020
STATUS
approved