OFFSET
0,1
COMMENTS
For a discussion and guide to related sequences, see A197739.
EXAMPLE
0.45929534126210755105483751035805264919200...
MATHEMATICA
b = 1; c = Pi;
f[x_] := Cos[b*x]^2; g[x_] := Sin[c*x]^2; s[x_] := f[x] + g[x];
r = x /. FindRoot[b*Sin[2 b*x] == c*Sin[2 c*x], {x, .45, .46}, WorkingPrecision -> 110]
RealDigits[r] (* A197821 *)
m = s[r]
RealDigits[m] (* A197822 *)
Plot[{b*Sin[2 b*x], c*Sin[2 c*x]}, {x, 0, Pi}]
d = m/2; t = x /. FindRoot[s[x] == d, {x, .7, .8}, WorkingPrecision -> 110]
RealDigits[t] (* A197823 *)
Plot[{s[x], d}, {x, 0, Pi}, AxesOrigin -> {0, 0}]
d = m/3; t = x /. FindRoot[s[x] == d, {x, .8, .9}, WorkingPrecision -> 110]
RealDigits[t] (* A197824 *)
Plot[{s[x], d}, {x, 0, Pi}, AxesOrigin -> {0, 0}]
d = 1; t = x /. FindRoot[s[x] == d, {x, .7, .8}, WorkingPrecision -> 110]
RealDigits[t] (* A197726 *)
Plot[{s[x], d}, {x, 0, Pi}, AxesOrigin -> {0, 0}]
d = 1/2; t = x /. FindRoot[s[x] == d, {x, .89, 9.1}, WorkingPrecision -> 110]
RealDigits[t] (* A197826 *)
Plot[{s[x], d}, {x, 0, Pi}, AxesOrigin -> {0, 0}]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 19 2011
EXTENSIONS
Definition corrected by Georg Fischer, Aug 10 2021
STATUS
approved