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Results tagged with legendre-polynomials
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user 136807
4
votes
1
answer
206
views
Integral with Legendre polynomial
Let $n$ be an integer $\geq 2$ and let $p_n(x)=\displaystyle \frac{1}{n!}(x^n(1-x)^n)^{(n)}$ be a Legendre polynomial.
Let $k $ be a positive integer.
I would like know if there is a closed formula …
- 417
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