A019683 Decimal expansion of Pi/16.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Examples

			Pi/16 = 0.19634954084936207740391521145496893026232308746094411381... - _Vladimir Joseph Stephan Orlovsky_, Dec 02 2009
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.4.2, p. 494.

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Index entries for transcendental numbers.

Crossrefs

Cf. A157332, A000796, A003881, A019669, A019670, A019675, A019679, A244978.

Programs

Magma

R:= RealField(100); Pi(R)/16; // G. C. Greubel, Aug 26 2019

Mathematica

RealDigits[N[Pi/16,6! ]] (* Vladimir Joseph Stephan Orlovsky, Dec 02 2009 *)

PARI

default(realprecision, 100); Pi/16 \\ G. C. Greubel, Aug 26 2019

Sage

numerical_approx(pi/16, digits=100) # G. C. Greubel, Aug 26 2019

Formula

From Peter Bala, Oct 27 2019: (Start)

Equals Integral_{x = 0..1} x^2*sqrt(1 - x^2) dx = Integral_{x = 0..1} x^3*sqrt(1 - x^8) dx.

Equals Integral_{x = 0..inf} x^2/(1 + x^2)^3 dx. (End)

From Amiram Eldar, Aug 04 2020: (Start)

Equals Sum_{k>=1} sin(k)^3 * cos(k)/k.

Equals Sum_{k>=1} sin(k)^3 * cos(k)^2/k.

Equals Sum_{k>=1} (-1)^(k+1) * sin((2*k-1)/4)/(2*k-1)^2. (End)