<![CDATA[Math Is Fun Forum / Abel Summation (Summation by Parts)]]>2015-10-24T08:22:58ZFluxBBhttp://www.mathisfunforum.com/viewtopic.php?id=22630<![CDATA[Abel Summation (Summation by Parts)]]>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 writing

where denotes the greatest integer part of x, and is the Euler-Mascheroni constant.]]>http://www.mathisfunforum.com/profile.php?id=2060892015-10-24T08:22:58Zhttp://www.mathisfunforum.com/viewtopic.php?pid=370036#p370036