A103714 Decimal expansion of the area of the surface generated by revolving one arch of the cosine curve about the x-axis.

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

Offset

2,2

Comments

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

References

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

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

Links

Table of n, a(n) for n=2..106.

Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2022, sec. 8.1.

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

Sylvester Reese and Jonathan Sondow, MathWorld: Universal Parabolic Constant.

Wikipedia, Universal parabolic constant.

Formula

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

Example

14.423599448414093929375465539601335358054115235952...

Mathematica

RealDigits[2*Pi*(Sqrt[2] + Log[1 + Sqrt[2]]), 10, 120][[1]] (* Amiram Eldar, May 31 2023 *)

Crossrefs

Cf. 2*A000796*A103710. See also A103713.

Sequence in context: A068923 A222295 A371706 * A260486 A193514 A112108

Adjacent sequences: A103711 A103712 A103713 * A103715 A103716 A103717

Keyword

cons,easy,nonn

Author

Sylvester Reese and Jonathan Sondow, Feb 21 2005

Status

approved