A177218 Decimal expansion of the integral over cos(Pi*x)*x^(1/x) between 1/e and e.

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

Offset: 0

Author

Marvin Ray Burns, May 04 2010

Keywords

• nonn
• cons

Comments

Strangely close to A037077 which is a sum of the integrand from 1 to infinity.

Examples

			0.187779...
		

Links

• Marvin Ray Burns, Author's original inquiry
• R. J. Mathar, Numerical evaluation of the oscillatory integral over exp(i*pi*x)x^(1/x) between 1 and infinity, arXiv:0912.3844

Crossrefs

A157852 is the same integral from 1 to infinity.

Programs

Maple

Int( cos(Pi*x)*x^(1/x),x=exp(-1)..exp(1)) ; evalf(%) ; # R. J. Mathar, May 07 2010

Mathematica

RealDigits[ Re[NIntegrate[(-1)^n*n^(1/n), {n, 1/E, E}, WorkingPrecision -> 200]]]

Extensions

Definition simplified, keyword:cons inserted, offset corrected by R. J. Mathar, May 07 2010