From: rusin@vesuvius.math.niu.edu (Dave Rusin)
Newsgroups: sci.math.num-analysis
Subject: Re: applications of Stieltjes integrals
Date: 22 Jul 1998 21:30:09 GMT

In article <ylazpe4pbub.fsf@shekel.mcl.cs.columbia.edu>,
Art Werschulz  <agw@shekel.mcl.cs.columbia.edu> wrote:

>I'm trying to collect references to where Stieltjes integrals are used
>in more-or-less real applications.  If you know of any, please send
>them. 

The sci.math.num-analysis crowd might not consider this "more-or-less real"
but Stieltjes integrals are frequently used in analytic number theory.
If one needs to compute a sum of the values of some function  f(x) 
over the set of primes, one may express this as an integral of
f(x) d pi(x),  where  pi(x) is the function which counts the number of
primes less than or equal to  x. This is handy as  pi(x)  is roughly
the anti-derivative of  1/ln(x).

dave