A093828 Decimal expansion of (3*Pi)/8.

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

Offset: 1

Author

Eric W. Weisstein, Apr 16 2004

Keywords

• nonn
• cons
• easy

Comments

Area of an astroid with a = 1.

Examples

			1.1780972450961724644234912687298135815739385247656646...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Eric Weisstein's World of Mathematics, Astroid.
• Eric W. Weisstein, Euler's Series Transformation.
• Index entries for transcendental numbers

Crossrefs

Cf. A161685 (continued fraction). - Harry J. Smith, Jun 18 2009

Programs

Magma

SetDefaultRealField(RealField(110)); R:= RealField(); 3*Pi(R)/8; // G. C. Greubel, Aug 11 2019

Maple

evalf[110](3*Pi*(1/8)); # G. C. Greubel, Aug 11 2019

Mathematica

RealDigits[3*Pi/8, 10, 105][[1]] (* G. C. Greubel, Aug 11 2019 *)

PARI

{ default(realprecision, 20080); x=3*Pi/8; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b093828.txt", n, " ", d)); } \\ Harry J. Smith, Jun 18 2009

Sage

numerical_approx(3*pi/8, digits=110) # G. C. Greubel, Aug 11 2019

Formula

Equals Integral_{x>0} sin(x)^3/x^3. - Jean-François Alcover, Jun 04 2013

From Amiram Eldar, Aug 02 2020: (Start)

Equals arctan(1 + sqrt(2)).

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

Equals Sum_{k>=1} sin(k*Pi/4)/k. - Amiram Eldar, May 30 2021

3*Pi/8 = Sum_{n >= 1} n*(n+1)*2^(n+1)/binomial(2*n+6,n+3) (apply Euler's series transformation to the series representation Pi = 384*Sum_{n >= 1} (-1)^(n+1)*n^2/((4*n^2 - 1)*(4*n^2 - 9)*(4*n^2 - 25)) ). - Peter Bala, Dec 08 2021