Re: Did you hear about Euler-Mascheroni integrals?


"Joachim Selke" <selke@xxxxxx> wrote in message
news:erm9u5$h39$2@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Badger wrote:
I can't help with references to the specific term "Euler-Mascheroni
integrals", but I can give you some pointers to relevant material.

"Irresistible Integrals: Symbolics, Analysis and Experiments in the
Evaluation of Integrals" by Boros and Moll, ISBN 0521796369.

I looked into several books that deal with integrals. This one was one
of these. :-)

They also give (page 214) a recursion for what would be your I(n+1),
and refer to a book that contains the values up to what would be your
I(10), namely "Series Associated with the Zeta and Related Functions"
by Srivastava and Choi.

I tried to get this book but was not able to. There seems to be no
university library in northern Germany that owns this book. And due to
the high price I don't want to buy it ...

Proofs that are related to the integral you asked about include:
<http://www.math.tulane.edu/~vhm/web_html/gamma1web.pdf>
<http://www.math.tulane.edu/~vhm/web_html/explog1web.pdf>

I also know this documents already but I'm wondering why the term
Euler-Mascheroni integrals is not mentioned there. Now I suspect that
this name was "invented" by MathWorld.

All names have to be invented at some time. Presumably you mean that it has
no historical provenance.

Nick


.

Relevant Pages

  • Re: 22/7 - pi integral and a sci.math challenge
    ... The evaluation by hand is much simpler than it looks, ... but all 5 published solutions are extremely contrived: ... At the end is the following editorial note: ... Note quite what you were asking for, but the integrals int(x^n/ ...
    (sci.math)
  • Re: OT: Re: Xcas
    ... A friend commented to me that TI uses a system of tables of integrals ... that make the evaluation much more fast, and in fact it is it, because ... Fortunately, I have improved this on Xcas,x)) ...
    (comp.sys.hp48)
  • Re: 22/7 - pi integral and a sci.math challenge
    ... The evaluation by hand is much simpler than it looks, ... Fall 1984, pp. 59-60], but all 5 published solutions ... to \pi Derived from Integrals with Nonnegative Integrands" by Stephen K. ...
    (sci.math)
  • Re: Did you hear about Euler-Mascheroni integrals?
    ... "Irresistible Integrals: Symbolics, ... Evaluation of Integrals" by Boros and Moll, ...
    (sci.math)
  • Re: Boros and Moll (2006)
    ... "Irresistible integrals" by Boros and Moll ... I use Maple and Mma 5.2. ...
    (sci.math.symbolic)