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##### 4: 30.14 Wave Equation in Oblate Spheroidal Coordinates
30.14.8 $w_{1}(\xi)=a_{1}S^{m(1)}_{n}\left(i\xi,\gamma\right)+b_{1}S^{m(2)}_{n}\left(i% \xi,\gamma\right).$
###### §30.14(v) The Interior Dirichlet Problem for Oblate Ellipsoids
30.14.9 $S^{m(1)}_{n}\left(\mathrm{i}\xi_{0},\gamma\right)=0.$
##### 5: 30.1 Special Notation
The main functions treated in this chapter are the eigenvalues $\lambda^{m}_{n}\left(\gamma^{2}\right)$ and the spheroidal wave functions $\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)$, $\mathsf{Qs}^{m}_{n}\left(x,\gamma^{2}\right)$, $\mathit{Ps}^{m}_{n}\left(z,\gamma^{2}\right)$, $\mathit{Qs}^{m}_{n}\left(z,\gamma^{2}\right)$, and $S^{m(j)}_{n}\left(z,\gamma\right)$, $j=1,2,3,4$. … Flammer (1957) and Abramowitz and Stegun (1964) use $\lambda_{mn}(\gamma)$ for $\lambda^{m}_{n}\left(\gamma^{2}\right)+\gamma^{2}$, $R_{mn}^{(j)}(\gamma,z)$ for $S^{m(j)}_{n}\left(z,\gamma\right)$, and …
##### 6: 30.13 Wave Equation in Prolate Spheroidal Coordinates
30.13.14 $w_{1}(\xi)=a_{1}S^{m(1)}_{n}\left(\xi,\gamma\right)+b_{1}S^{m(2)}_{n}\left(\xi% ,\gamma\right).$
30.13.15 $S^{m(1)}_{n}\left(\xi_{0},\gamma\right)=0.$
##### 7: Bibliography H
• S. Hanish, R. V. Baier, A. L. Van Buren, and B. J. King (1970) Tables of Radial Spheroidal Wave Functions, Vols. 1-3, Prolate, $m=0,1,2$; Vols. 4-6, Oblate, $m=0,1,2$ . Technical report Naval Research Laboratory, Washington, D.C..
• ##### 8: Bibliography B
• T. A. Beu and R. I. Câmpeanu (1983b) Prolate radial spheroidal wave functions. Comput. Phys. Comm. 30 (2), pp. 177–185.
• ##### 9: Bibliography C
• W. C. Connett, C. Markett, and A. L. Schwartz (1993) Product formulas and convolutions for angular and radial spheroidal wave functions. Trans. Amer. Math. Soc. 338 (2), pp. 695–710.
• ##### 10: Bibliography V
• A. L. Van Buren, R. V. Baier, S. Hanish, and B. J. King (1972) Calculation of spheroidal wave functions. J. Acoust. Soc. Amer. 51, pp. 414–416.
• A. L. Van Buren, R. V. Baier, and S. Hanish (1970) A Fortran computer program for calculating the oblate spheroidal radial functions of the first and second kind and their first derivatives. NRL Report No. 6959 Naval Res. Lab.  Washingtion, D.C..
• A. L. Van Buren and J. E. Boisvert (2002) Accurate calculation of prolate spheroidal radial functions of the first kind and their first derivatives. Quart. Appl. Math. 60 (3), pp. 589–599.
• A. L. Van Buren and J. E. Boisvert (2004) Improved calculation of prolate spheroidal radial functions of the second kind and their first derivatives. Quart. Appl. Math. 62 (3), pp. 493–507.
• Van Buren (website) Mathieu and Spheroidal Wave Functions: Fortran Programs for their Accurate Calculation