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Results tagged with ca.classical-analysis-and-odes
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user 89713
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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Expansion of the associated Legendre polynomials $P^m_l(\cos\vartheta)$ for $\vartheta \righ...
For completeness, here are the slightly modified expressions for $m<0$:
$$a_{lm}={1\over 2^{-m} (-m)!},$$
as well as the corresponding coefficients for the limit of $x\rightarrow -1$ or $\vartheta \ri …
- 369
1
vote
2
answers
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Expansion of the associated Legendre polynomials $P^m_l(\cos\vartheta)$ for $\vartheta \righ...
A simple test with Mathematica indicates that for the associated Legendre polynomials $P^m_l$ the following relation should hold:
$$ \lim_{\vartheta\rightarrow 0} P^m_l(\cos\vartheta) =a_{lm} \varthet …
- 369