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Results tagged with legendre-polynomials
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user 134299
5
votes
Accepted
Generating function of the product of Legendre polynomials
Using the recursion relation
$$
P_{n-1} (x) = x P_n (x) - \frac{x^2 -1}{n} \frac{d}{dx} P_n (x) \ ,
$$
you can reduce your expression to a sum of the generating function you quote and a combined deriv …
- 6,696
2
votes
Accepted
A recurrence formula for the Legendre function $P_\mu^\nu(x)$
Let's take relation 14.10.3 from the NIST Handbook, which, after renaming $\mu \leftrightarrow \nu $ and shifting the new $\mu \rightarrow \mu -2$ reads
$$
(\mu -\nu ) P_{\mu }^{\nu } (x) - (2\mu -1)x …
- 6,696