A019706 Decimal expansion of sqrt(Pi)/4.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Examples

			0.44311346272637900682454187083528629569938736403059678...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• I. S. Gradsteyn and I. M. Ryzhik, Table of integrals, series and products, (1980), page 420 (formulas 3.757.1, 3.757.2).
• Index entries for transcendental numbers

Crossrefs

Cf. A019683.

Programs

Maple

evalf(sqrt(Pi)/4,120); # Muniru A Asiru, Sep 22 2018

Mathematica

First[RealDigits[Sqrt[Pi]/4, 10, 100]] (* Paolo Xausa, May 02 2024 *)

PARI

sqrt(Pi)/4 \\ Altug Alkan, Sep 22 2018

PARI

intnum(x=0, [oo, -8*I], sin(8*x)/sqrt(x)) \\ Gheorghe Coserea, Sep 23 2018

PARI

intnum(x=[0, -1/2], [oo, 8*I], cos(8*x)/sqrt(x)) \\ Gheorghe Coserea, Sep 23 2018

Formula

Equals sqrt(A019683). - Michel Marcus, Aug 31 2014

From A.H.M. Smeets, Sep 22 2018: (Start)

Equals Integral_{x >= 0} sin(8x)/sqrt(x) dx [Gradshteyn and Ryzhik].

Equals Integral_{x >= 0} cos(8x)/sqrt(x) dx [Gradshteyn and Ryzhik]. (End)

From Amiram Eldar, Aug 13 2020: (Start)

Equals Integral_{x=0..oo} x * exp(-x^4) dx.

Equals Integral_{x=0..oo} x^2 * exp(-x^2) dx. (End)