A103713 Decimal expansion of the area of the surface generated by revolving about the y-axis that part of the curve y = log x lying in the 4th quadrant.

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

Offset

1,1

Comments

Equal to Pi times its analog for the parabola (see A103710).

References

C. E. Love, Differential and Integral Calculus, 4th ed., Macmillan, 1950, p. 288.

S. Reese, A universal parabolic constant, 2004, preprint.

Links

Table of n, a(n) for n=1..105.

S. R. Finch, Mathematical Constants, addenda, sec. 8.1

S. Reese, Pohle Colloquium Video Lecture: The universal parabolic constant, February 2, 2005

S. Reese and J. Sondow, MathWorld: Universal Parabolic Constant

Wikipedia, Universal parabolic constant

Formula

Pi*(sqrt(2) + log(1 + sqrt(2))).

Example

7.21179972420704696468773276980066767902705761797605...

Mathematica

RealDigits[Pi*(Sqrt[2]+Log[1+Sqrt[2]]), 10, 120][[1]] (* or *) RealDigits[Pi* (Sqrt[2]+ArcSinh[1]), 10, 120][[1]] (* Harvey P. Dale, May 02 2011 *)

Prog

(PARI) Pi*(sqrt(2) + log(1 + sqrt(2))) \\ Michel Marcus, Jul 06 2015

Crossrefs

Cf. A000796*A103710. See also A103714.

Sequence in context: A001204 A177969 A021585 * A197184 A089129 A100957

Adjacent sequences: A103710 A103711 A103712 * A103714 A103715 A103716

Keyword

cons,easy,nonn

Author

Sylvester Reese and Jonathan Sondow, Feb 21 2005

Status

approved