A217732 Decimal expansion of integral_{x=0..infinity} 1/(cos(x) + x^2) dx.

1, 8, 3, 8, 0, 1, 7, 6, 9, 5, 0, 1, 0, 5, 0, 3, 8, 5, 2, 6, 9, 5, 3, 1, 4, 3, 9, 8, 1, 3, 9, 9, 2, 9, 2, 6, 8, 4, 3, 3, 0, 8, 6, 5, 3, 3, 0, 1, 2, 6, 3, 1, 3, 9, 4, 2, 5, 6, 9, 9, 1, 8, 9, 8, 2, 2, 8, 8, 0, 0, 9, 0, 5, 5, 5, 2, 9, 1, 8, 2, 2, 2, 7, 8, 6, 1, 0, 6, 1, 3, 5, 4, 9, 7, 7, 0, 1, 1, 9, 5

Offset

1,2

Comments

What is most interesting is the way Richard Easther (from Columbia University in 2001) tackles the evaluation of this tough integral.

Links

Table of n, a(n) for n=1..100.

Richard Easther, A tough integral, MathGroup archive 2001.

Example

1.8380176950105038526953143981399292684330865330126313942569918982...

Mathematica

digits = 100; s = Sum[1/(Cos[x] + (x + n*2*Pi)^2), {n, 0, Infinity}]; NIntegrate[s, {x, 0, 2*Pi}, WorkingPrecision -> digits] // RealDigits[#, 10, digits]& // First (* after Richard Easther *)

Crossrefs

Sequence in context: A011214 A119806 A248296 * A089260 A109866 A097079

Adjacent sequences: A217729 A217730 A217731 * A217733 A217734 A217735

Keyword

nonn,cons

Author

Jean-François Alcover, Mar 22 2013

Status

approved