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30 Spheroidal Wave FunctionsComputation

§30.17 Tables

  • Stratton et al. (1956) tabulates quantities closely related to λnm(γ2) and an,km(γ2) for 0m8, mn8, 64γ264. Precision is 7S.

  • Flammer (1957) includes 18 tables of eigenvalues, expansion coefficients, spheroidal wave functions, and other related quantities. Precision varies between 4S and 10S.

  • Hanish et al. (1970) gives λnm(γ2) and Snm(j)(z,γ), j=1,2, and their first derivatives, for 0m2, mnm+49, 1600γ21600. The range of z is given by 1z10 if γ2>0, or z=iξ, 0ξ2 if γ2<0. Precision is 18S.

  • EraŠevskaja et al. (1973, 1976) gives Sm(j)(iy,ic), Sm(j)(z,γ) and their first derivatives for j=1,2, 0.5c8, y=0,0.5,1,1.5, 0.5γ8, z=1.01,1.1,1.4,1.8. Precision is 15S.

  • Van Buren et al. (1975) gives λn0(γ2), 𝖯𝗌n0(x,γ2) for 0n49, 1600γ21600, 1x1. Precision is 8S.

  • Zhang and Jin (1996) includes 24 tables of eigenvalues, spheroidal wave functions and their derivatives. Precision varies between 6S and 8S.

Fletcher et al. (1962, §22.28) provides additional information on tables prior to 1961.