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Results tagged with integration
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user 136807
Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...
3
votes
1
answer
239
views
Looking for bound in integral involving Legendre polynomial
I'm looking for an upper bound to the following integral or equivalent when $n$ leads to $ +\infty $ to the following expression
$$I_n:=\left|\int_{0}^1 \int_{0}^1 \frac{p_n(x) p_n(y)}{(1-xy)} dx dy …
- 417
2
votes
0
answers
149
views
A bound using Cauchy formula
Let $0<t_0<1$ fixed number , $ n_0$ integer $ \geq 2$ fixed and let $\forall 0<u<1, f(u)= \displaystyle \frac{(1-u)^{n_0} \log(1-u)}{(1-ut_0)^{n_0+1}} $.
Let $0<u_0<1 $ be given. I'm looking a go …
- 417
0
votes
0
answers
60
views
Integral involving legendre (as Beukers integral) [duplicate]
let $\forall n $ integer $p_n(t)=\frac{1}{n!}(t^n(1-t)^n)^{(n)} $
i 'm looking for an explicit constant $0<c<1$ ( very good small c ) independant of $n$, and a constant $b$ ( non explicit) independa …
- 417
-1
votes
1
answer
154
views
About a multiple integral [closed]
,w,t)\mathrm{d}u \mathrm{d}v \mathrm{d}w \mathrm{d}t
\end{split}
$$
What theorem (be it a necessary and sufficient or only a sufficient condition) would allow me to perform any change of the order of integration …
- 417