A115754 Decimal expansion of sqrt(3/2).

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

Offset: 1

Author

Eric Desbiaux, Jul 30 2008

Keywords

• nonn
• easy
• cons

Comments

Coordinate of a control point for a degree-5 integration formula for 7 points over the unit circle. [Stroud & Secrest]

Also real and imaginary part of sqrt(-3i). - Alonso del Arte, Dec 11 2012

Area of the quadrilateral obtained when slicing a unit cube with a plane passing through opposite vertices and the middle of opposite edges. See CNRS link. - Michel Marcus, Mar 26 2016

Positive zero of the Hermite polynomial of degree 3. - A.H.M. Smeets, Jun 02 2025

Examples

			1.2247448713915890490986420373529456959829737403283350642163...
		

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
• Ana Rechtman, Mars 2016, 3e défi, Images des Mathématiques, CNRS, 2016.
• A. H. Stroud and D. Secrest, Approximate integration formulas for certain spherically symmetric regions, Math. Comp. 17 (82) (1963) 105.
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A382713 (continued fraction), A068388 (Engel expansion).

Cf. A010464 (double), A187110 (half), A157697 (reciprocal).

Programs

Mathematica

RealDigits[Sqrt[3/2], 10, 105][[1]] (* Alonso del Arte, Dec 11 2012 *)

Formula

Equals 2*A187110.

Equals Sum_{k>=0} binomial(1/2, k)/2^k. - Bruno Berselli, Sep 11 2015

From Amiram Eldar, Aug 02 2020: (Start)

Equals Product_{k>=0} (1 + (-1)^k/(6*k + 3)).

Equals Sum_{k>=0} binomial(2*k,k)/12^k.

Equals 1 + Sum_{k>=1} (2*k - 1)!!/((2*k)!! * 3^k). (End)

Equals A010464/2. - R. J. Mathar, Feb 23 2021