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A103713
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Decimal expansion of the area of the surface generated by revolving about the y-axis that part of the curve y = ln x lying in the 4th quadrant.
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1
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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
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Equal to pi times its analogue for the parabola (see A103710).
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REFERENCES
| C. E. Love, Differential and Integral Calculus, 4th ed., Macmillan, 1950, p. 288.
S. Reese, A universal parabolic constant, 2004, preprint.
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LINKS
| S. R. Finch, Mathematical Constants, addenda, sec. 8.1
S. Reese, Pohle Colloquium Video Lecture: The universal parabolic constant, February 2, 2005
Eric Weisstein's World of Mathematics, Universal Parabolic Constant
Wikipedia, Universal parabolic constant
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FORMULA
| pi*(sqrt(2) + ln(1 + sqrt(2))).
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EXAMPLE
| 7.2117997242070469646877327698006676790270576179761...
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MATHEMATICA
| RealDigits[Pi*(Sqrt[2]+Log[1+Sqrt[2]]), 10, 120][[1]] (* or *) RealDigits[Pi* (Sqrt[2]+ArcSinh[1]), 10, 120][[1]] (* From Harvey P. Dale, May 02 2011 *)
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CROSSREFS
| Cf. A000796*A103710. See also A103714.
Sequence in context: A001204 A177969 A021585 * A197184 A089129 A100957
Adjacent sequences: A103710 A103711 A103712 * A103714 A103715 A103716
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KEYWORD
| cons,easy,nonn
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AUTHOR
| Sylvester Reese and Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Feb 21 2005
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