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#1 2015-10-23 20:22:58

zetafunc
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Registered: 2014-05-21
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Abel Summation (Summation by Parts)

ABEL SUMMATION: The Continuous Version of the Summation by Parts Formula

Let
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.

Last edited by zetafunc (2015-10-27 07:22:34)

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