If 
is positive and decreases to 0, then an Euler constant
![gamma_f=lim_(n->infty)[sum_(k=1)^nf(k)-int_1^nf(x)dx]](/images/equations/Maclaurin-CauchyTheorem/NumberedEquation1.svg) |
can be defined.
For example, if 
, then
 |
which is just the usual Euler-Mascheroni constant.
Maclaurin-Cauchy Theorem
See also
Euler-Maclaurin Integration Formulas, Euler-Mascheroni Constant, Numerical DifferentiationExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Maclaurin-Cauchy Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Maclaurin-CauchyTheorem.html