A321120 Decimal expansion of (3 + sqrt(3))/12.

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

Offset: 0

Author

Franck Maminirina Ramaharo, Nov 09 2018

Keywords

• nonn
• easy
• cons

Comments

The smallest weight in Holladay-Sard's quadrature formula for semi-infinite integrals.

Examples

			0.3943375672974064411272871951...
		

References

• Harold J. Ahlberg, Edwin N. Nilson and Joseph L. Walsh, The Theory of Splines and Their Applications, Academic Press, 1967.

Links

• John C. Holladay, A smoothest curve approximation, Math. Comp. Vol. 11 (1957), 233-243.
• Leroy F. Meyers and Arthur Sard, Best approximate integration formulas, J. Math. Phys. Vol. 29 (1950), 118-123.
• Arthur Sard, Best approximate integration formulas; best approximation formulas, American Journal of Mathematics Vol. 71 (1949), 80-91.
• Frans Schurer, On natural cubic splines, with an application to numerical integration formulae, EUT report. WSK, Dept. of Mathematics and Computing Science Vol. 70-WSK-04 (1970), 1-32.

Crossrefs

Cf. A020805, A165663.

Cf. A321118, A321119.

Programs

Maple

Digits := 1000; evalf((3 + sqrt(3))/12);

Mathematica

RealDigits[(3 + Sqrt[3])/12, 10, 100][[1]]

PARI

(3 + sqrt(3))/12

Formula

Equals lim_{n->infinity} A321118(0,n)/A321119(n).

Irrational number represented by the periodic continued fraction [0, 2, 1, 1; [6, 2]].

Largest real root of 1 - 12*x + 24*x^2.