OFFSET
1,1
COMMENTS
Let f(x)=sin(x)+cos(x) and g(x)=f(x)+f(2x)+...+f(nx), where n>=2. Then f(x) attains an absolute minimum at some x between 0 and 2*pi. Guide to related sequences (including graphs in Mathematica programs):
n....x.........minimum of f(x)
EXAMPLE
x=4.89312267296329905539673190581...
min=-2.09298678025110342592267820137...
MATHEMATICA
f[t_] := Sin[t] + Cos[t]
x = Minimize[f[t] + f[2 t], t]
N[x, 30]
(RealDigits[N[{#1[[1]], t /. #1[[2]]}, 110]] &)[x]
Plot[f[t] + f[2 t], {t, -3 Pi, 3 Pi}]
(* Second program: *)
Root[27 - 162x - 207x^2 + 8x^3 + 32x^4, 1] // RealDigits[#, 10, 99]& // First (* Jean-François Alcover, Feb 19 2013 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 29 2011
STATUS
approved