expansions in series of Ferrers functions

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11: 30.16 Methods of Computation

… ►For small $|{\gamma }^2|$ we can use the power-series expansion (30.3.8). …If $|{\gamma }^2|$ is large we can use the asymptotic expansions in §30.9. … ►If $|{\gamma }^2|$ is large, then we can use the asymptotic expansions referred to in §30.9 to approximate ${\mathrm{𝖯𝗌}}_n^m(x,{\gamma }^2)$. … ►A fourth method, based on the expansion (30.8.1), is as follows. … …