1,1

The continuous counterpart of 1^(1/1)-2^(1/2)+3^(1/3)-4^(1/4)...2*integer as n->infinity.

It is hard to integrate and very slow to converge.

From a numerical integration of the first 5 to 8 periods of the exp(i*pi*x) and estimation of the remainder with a mixed Filon-Euler-Maclaurin approach collecting up to the 5th order of the derivatives, we get 0.68765236884 (up to 6th order 0.68765236894, up to 7th order 0.68765236893), all numbers rounded. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 23 2009]

M. R. Burns, Used with other constants to converge closely to rational numbers.

M. R. Burns, Author's public inquiry 1

M. R. Burns, Author's public inquiry 2

After integrating from 1 to 5 Million the integral~= 0.6876533456.

After integrating from 1 to 10 Million the integral~= 0.6876528792.

After integrating from 1 to 15 Million the integral~= 0.6876527177.

After integrating from 1 to 20 Million the integral~= 0.6876526145.

Integrating A037077 instead of summing.

Sequence in context: A092294 A097668 A133748 this_sequence A088608 A011481 A100221

Adjacent sequences: A157849 A157850 A157851 this_sequence A157853 A157854 A157855

nonn,more

Marvin Ray Burns (bmmmburns(AT)sbcglobal.net), Mar 07 2009, Mar 11 2009, Mar 13 2009

Edited by N. J. A. Sloane, Mar 13 2009

Corrected and edited by Marvin Ray Burns (bmmmburns(AT)sbcglobal.net), Apr 03 2009