Digital Library of Mathematical Functions
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30 Spheroidal Wave FunctionsComputation

§30.17 Tables

  • Stratton et al. (1956) tabulates quantities closely related to \mathop{\lambda^{{m}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right) and a^{m}_{{n,k}}(\gamma^{2}) for 0\leq m\leq 8, m\leq n\leq 8, -64\leq\gamma^{2}\leq 64. 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 \mathop{\lambda^{{m}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right) and \mathop{S^{{m(j)}}_{{n}}\/}\nolimits\!\left(z,\gamma\right), j=1,2, and their first derivatives, for 0\leq m\leq 2, m\leq n\leq m+49, -1600\leq\gamma^{2}\leq 1600. The range of z is given by 1\leq z\leq 10 if \gamma^{2}>0, or z=-i\xi, 0\leq\xi\leq 2 if \gamma^{2}<0. Precision is 18S.

  • EraŠevskaja et al. (1973, 1976) gives \mathop{S^{{m(j)}}\/}\nolimits\!\left(iy,-ic\right), \mathop{S^{{m(j)}}\/}\nolimits\!\left(z,\gamma\right) and their first derivatives for j=1,2, 0.5\leq c\leq 8, y=0,0.5,1,1.5, 0.5\leq\gamma\leq 8, z=1.01,1.1,1.4,1.8. Precision is 15S.

  • Van Buren et al. (1975) gives \mathop{\lambda^{{0}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right), \mathop{\mathsf{Ps}^{{0}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right) for 0\leq n\leq 49, -1600\leq\gamma^{2}\leq 1600, -1\leq x\leq 1. 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.

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