proof that Euler’s constant exists
Now, by considering the Taylor series for , we see that
Thus, the decrease monotonically, while the increase monotonically, since the differences are negative (positive for ). Further, and thus is a lower bound for . Thus the are monotonically decreasing and bounded below, so they must converge.
- 1 E. Artin, The Gamma Function, Holt, Rinehart, Winston 1964.
|Title||proof that Euler’s constant exists|
|Date of creation||2013-03-22 16:34:48|
|Last modified on||2013-03-22 16:34:48|
|Last modified by||rm50 (10146)|