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Results tagged with legendre-polynomials
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user 94200
7
votes
2
answers
5k
views
Legendre Polynomial Integral
How can I evaluate
$$ \int_{-1}^1 P_n(x)P_l(x)x^k dx $$
when $k$ is even?
Or what might be a source where I could find integrals like this?
- 573
1
vote
0
answers
182
views
Expansion of prolate spheroidal harmonics
For two coordinate frames $O'$ and $O''$ both offset along the $z$-axis by $\pm R$ respectively, with corresponding offset spherical coordinates $r'$, $\theta'$, $r''$ and $\theta''$, and with prolate …
- 573
5
votes
2
answers
3k
views
Relation between Legendre and Chebyshev polynomials
Where I could find relationships between Legendre and Chebyshev polynomials?
For example I found with maple
$$ P_n(\cos\theta)=\sum_{k=0}^n(-1)^{n+k}\frac{2-\delta_{k0}}{4^n}
\binom{n-k}{\frac{n-k}{2 …
- 573