A127196 Decimal expansion of value of the Glasser-Oloa integral: Integral_{x=0..Pi/2} x^2/(x^2 + log(2*cos(x))^2) dx.

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

Offset

0,1

Comments

The ZbMATH reviewer calls Oloa's formula a "remarkable integral." - Jonathan Sondow, Mar 02 2014

References

Olivier Oloa, Some Euler-Type Integrals and a New Rational Series for Euler's Constant, Contemp. Math., 457 (2008), 253-264.

Links

Table of n, a(n) for n=0..104.

T. Amdeberhan, O. Espinosa, and V. Moll, The Laplace transform of the digamma function: An integral due to Glasser, Manna and Oloa, Proc. Amer. Math. Soc., 136 (2008), 3211-3221.

Per W. Karlsson, Review of "Some Euler-Type Integrals and a New Rational Series for Euler's Constant" by O. Oloa, ZbMATH

Eric Weisstein's World of Mathematics, Definite Integral

Formula

(Pi*(1 - EulerGamma + log(2*Pi)))/8.

Example

0.88775965640386875842...

Mathematica

RealDigits[(Pi(1-EulerGamma+Log[2Pi]))/8, 10, 120][[1]] (* Harvey P. Dale, Jan 20 2013 *)

Crossrefs

Sequence in context: A202953 A088661 A329220 * A350715 A294795 A173623

Adjacent sequences: A127193 A127194 A127195 * A127197 A127198 A127199

Keyword

nonn,cons

Author

Eric W. Weisstein, Jan 07 2007

Status

approved