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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.

%I A103713 #30 Feb 16 2025 08:32:56
%S A103713 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,
%T A103713 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,
%U A103713 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
%N 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.
%C A103713 Equal to Pi times its analog for the parabola (see A103710).
%D A103713 C. E. Love, Differential and Integral Calculus, 4th ed., Macmillan, 1950, p. 288.
%D A103713 S. Reese, A universal parabolic constant, 2004, preprint.
%H A103713 S. R. Finch, <a href="http://arxiv.org/abs/2001.00578">Mathematical Constants, addenda, sec. 8.1</a>
%H A103713 S. Reese, <a href="http://gaia.adelphi.edu/cgi-bin/makehtmlmov-css.pl?rtsp://gaia.adelphi.edu:554/General_Lectures/Pohle_Colloquiums/pohle200502.mov,pohle200502.mov,256,200">Pohle Colloquium Video Lecture: The universal parabolic constant, February 2, 2005</a>
%H A103713 S. Reese and J. Sondow, <a href="https://mathworld.wolfram.com/UniversalParabolicConstant.html">MathWorld: Universal Parabolic Constant</a>
%H A103713 Wikipedia, <a href="http://en.wikipedia.org/wiki/Universal_parabolic_constant">Universal parabolic constant</a>
%F A103713 Pi*(sqrt(2) + log(1 + sqrt(2))).
%e A103713 7.21179972420704696468773276980066767902705761797605...
%t A103713 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 *)
%o A103713 (PARI) Pi*(sqrt(2) + log(1 + sqrt(2))) \\ _Michel Marcus_, Jul 06 2015
%Y A103713 Cf. A000796*A103710. See also A103714.
%K A103713 cons,easy,nonn
%O A103713 1,1
%A A103713 Sylvester Reese and _Jonathan Sondow_, Feb 21 2005