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
Examples
7.21179972420704696468773276980066767902705761797605...
References
- C. E. Love, Differential and Integral Calculus, 4th ed., Macmillan, 1950, p. 288.
- S. Reese, A universal parabolic constant, 2004, preprint.
Links
- 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
Programs
-
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 *)
-
PARI
Pi*(sqrt(2) + log(1 + sqrt(2))) \\ Michel Marcus, Jul 06 2015
Formula
Pi*(sqrt(2) + log(1 + sqrt(2))).
Comments