

A103713


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


1



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
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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

7.2117997242070469646877327698006676790270576179761...


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



