Prove que/prove that
where/em que 
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1.º Problema de 2010: um integral de Stieltjes :: 2010 Problem #1 – A Stieltjes Integral
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Wouldn’t there be a problem if
?
According to my evaluation
Also, I am having a little difficulty in understanding the right hand side expression. Isn’t there supposed to be some summation sign? I mean,
should be summed over 
, is that right (of course, not allowing 
)?
What I mean is this: prove that the given integral can be expressed as a racional multiple of
, i. e. 
.
I edited the problem statement a little bit.
Ah, I see now. Thanks for the clarification. But, I must say that the integral in its present form is somewhat easy to calculate.
Then you can move to the last one. That is an important intermediate result. One gets
expressed as another series that converges faster to 
(see e.g. van der Poorten’s paper A proof Euler missed…, Apéry’s proof of the irrationality of 
, An informal report). You find it online. Go to the page Consulta de publicações.
PS. I think that most of my readers doesn’t even know what a Stiltjes integral is.