for prolate spheroids

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1—10 of 15 matching pages

1: Bibliography X
• H. Xiao, V. Rokhlin, and N. Yarvin (2001) Prolate spheroidal wavefunctions, quadrature and interpolation. Inverse Problems 17 (4), pp. 805–838.
3: Bibliography V
• A. L. Van Buren, B. J. King, R. V. Baier, and S. Hanish (1975) Tables of Angular Spheroidal Wave Functions, Vol. 1, Prolate, $m=0$; Vol. 2, Oblate, m=0. Naval Res. Lab. Reports, Washington, 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.
5: 30.2 Differential Equations
In applications involving prolate spheroidal coordinates $\gamma^{2}$ is positive, in applications involving oblate spheroidal coordinates $\gamma^{2}$ is negative; see §§30.13, 30.14. …
7: 30.4 Functions of the First Kind
When $\gamma^{2}>0$ $\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)$ is the prolate angular spheroidal wave function, and when $\gamma^{2}<0$ $\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)$ is the oblate angular spheroidal wave function. If $\gamma=0$, $\mathsf{Ps}^{m}_{n}\left(x,0\right)$ reduces to the Ferrers function $\mathsf{P}^{m}_{n}\left(x\right)$: …
8: Bibliography S
• D. Slepian and H. O. Pollak (1961) Prolate spheroidal wave functions, Fourier analysis and uncertainty. I. Bell System Tech. J. 40, pp. 43–63.
• D. Slepian (1964) Prolate spheroidal wave functions, Fourier analysis and uncertainity. IV. Extensions to many dimensions; generalized prolate spheroidal functions. Bell System Tech. J. 43, pp. 3009–3057.
• 9: 14.30 Spherical and Spheroidal Harmonics
$P^{m}_{n}\left(x\right)$ and $Q^{m}_{n}\left(x\right)$ ($x>1$) are often referred to as the prolate spheroidal harmonics of the first and second kinds, respectively. …
10: Bibliography M
• J. W. Miles (1975) Asymptotic approximations for prolate spheroidal wave functions. Studies in Appl. Math. 54 (4), pp. 315–349.
• H. J. W. Müller (1963) Asymptotic expansions of prolate spheroidal wave functions and their characteristic numbers. J. Reine Angew. Math. 212, pp. 26–48.