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solve-the-associated-legendre-equation-l-l-1-2-l-0-1-2-and-m-2-l-l-1-which-requires-l-m-l-using-power-series-




Question Number 200022 by jlewis last updated on 12/Nov/23
solve the associated legendre equation  λ=l (l+1)η^2  ;l=0,1,2...   and m^2 ≤ l(l+1)   which requires −l≤m≤l using power series
$$\mathrm{solve}\:\mathrm{the}\:\mathrm{associated}\:\mathrm{legendre}\:\mathrm{equation} \\ $$$$\lambda={l}\:\left({l}+\mathrm{1}\right)\eta^{\mathrm{2}} \:;{l}=\mathrm{0},\mathrm{1},\mathrm{2}…\:\:\:{and}\:{m}^{\mathrm{2}} \leqslant\:{l}\left({l}+\mathrm{1}\right)\: \\ $$$${which}\:{requires}\:−{l}\leqslant{m}\leqslant{l}\:\mathrm{using}\:\mathrm{power}\:\mathrm{series} \\ $$

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