A197692 Decimal expansion of (Pi^2)/(2+4*Pi).

6, 7, 7, 5, 6, 0, 9, 8, 3, 6, 0, 9, 7, 4, 9, 9, 3, 1, 0, 0, 8, 9, 6, 2, 3, 8, 6, 5, 3, 3, 4, 5, 6, 8, 8, 7, 9, 4, 9, 8, 0, 4, 0, 4, 0, 9, 4, 4, 4, 8, 3, 1, 6, 7, 0, 9, 2, 1, 5, 9, 1, 1, 2, 5, 5, 2, 0, 1, 3, 3, 7, 3, 6, 5, 2, 1, 2, 1, 4, 7, 3, 1, 3, 8, 7, 0, 3, 5, 2, 9, 4, 8, 4, 9, 8, 2, 7, 7, 9

Offset: 0

Author

Clark Kimberling, Oct 17 2011

Keywords

• nonn
• cons

Comments

Least x>0 such that sin(bx)=cos(cx) (and also sin(cx)=cos(bx)), where b=2 and c=1/Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			0.6775609836097499310089623865334568879498040...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A197682.

Programs

Maple

evalf((Pi^2)/(2+4*Pi),100); # Wesley Ivan Hurt, Feb 12 2017

Mathematica

b = 2; c = 1/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .6, .7}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197692 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 1}]

PARI

Pi^2/(2+4*Pi) \\ Michel Marcus, Feb 13 2017