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
S. R. Finch, Mathematical Constants, addenda, sec. 8.1
S. Reese and J. Sondow, MathWorld: Universal Parabolic Constant
Wikipedia, Universal parabolic constant
FORMULA
Pi*(sqrt(2) + log(1 + sqrt(2))).
EXAMPLE
7.21179972420704696468773276980066767902705761797605...
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
KEYWORD
AUTHOR
Sylvester Reese and Jonathan Sondow, Feb 21 2005
STATUS
approved