ABEL SUMMATION: The Continuous Version of the Summation by Parts FormulaLet be an arithmetic function. Denote the partial sums of a by:
Let , and suppose that is a continuously differentiable function on . Then:One of the many applications of this theorem is using it to show that:
by writingwhere denotes the greatest integer part of x, and is the Euler-Mascheroni constant.
Last edited by zetafunc (2015-10-27 07:22:34)