A197694 Decimal expansion of Pi/(4 + Pi).

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

Offset

0,1

Comments

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

Force per unit width, normalized by rho V^2 L, of an infinitely wide two-dimensional stream of inviscid fluid impinging on a plate of length L oriented normal to the stream (Lamb 1945). Here rho is the density of the fluid and V is the velocity of the stream. - Chris R. Rehmann, Dec 27 2025

References

H. Lamb, Hydrodynamics, Dover Publications, 1945, Article 76.

Links

Table of n, a(n) for n=0..98.

Index entries for transcendental numbers

Example

0.4399008464884426240895213745137133837991874432...

Mathematica

b = 2; c = Pi/2;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .4, .45}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197694 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 1.1}]

Crossrefs

Cf. A197682.

Sequence in context: A379064 A131805 A390092 * A187770 A103218 A319311

Adjacent sequences: A197691 A197692 A197693 * A197695 A197696 A197697

Keyword

nonn,cons

Author

Clark Kimberling, Oct 17 2011

Status

approved