spheroidal wave functions

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21—30 of 37 matching pages

22: Bibliography V

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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.

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External Links:: Document, ZentralBlatt
Referenced by:: §30.16(ii), §30.18(iii).
Encodings:: BibTeX

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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..

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Referenced by:: 5th item.
Encodings:: BibTeX

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Van Buren (website) Mathieu and Spheroidal Wave Functions: Fortran Programs for their Accurate Calculation

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External Links:: Home Page
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index, A. L. Van Buren and J. E. Boisvert (2002), A. L. Van Buren and J. E. Boisvert (2004), A. L. Van Buren and J. E. Boisvert (2007).
Encodings:: BibTeX

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23: 30.13 Wave Equation in Prolate Spheroidal Coordinates

§30.13 Wave Equation in Prolate Spheroidal Coordinates

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30.13.13

w_{2}(\eta)=a_{2}\mathsf{Ps}^{m}_{n}\left(\eta,\gamma^{2}\right)+b_{2}\mathsf{% Qs}^{m}_{n}\left(\eta,\gamma^{2}\right).

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Symbols:: $\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the first kind, $\mathsf{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the second kind, $m$ : nonnegative integer, $n\geq m$ : integer degree, $b_{j}$ : coefficients, $\eta$ : prolate spheroidal coordinate, $w_{j}$ : solution to DE, $\gamma^{2}=\kappa^{2}c^{2}$ : parameter and $a_{j}$ : coefficients
Referenced by:: §30.13(v), §30.14(iv), §30.14(v)
Permalink:: http://dlmf.nist.gov/30.13.E13
Encodings:: pMML, png, TeX
See also:: Annotations for §30.13(iv), §30.13 and Ch.30

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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).

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Symbols:: $S^{\NVar{m}(\NVar{j})}_{\NVar{n}}\left(\NVar{z},\NVar{\gamma}\right)$ : radial spheroidal wave function, $m$ : nonnegative integer, $n\geq m$ : integer degree, $\xi$ : prolate spheroidal coordinate, $b_{j}$ : coefficients, $w_{j}$ : solution to DE, $\gamma^{2}=\kappa^{2}c^{2}$ : parameter and $a_{j}$ : coefficients
Referenced by:: §30.13(v)
Permalink:: http://dlmf.nist.gov/30.13.E14
Encodings:: pMML, png, TeX
See also:: Annotations for §30.13(iv), §30.13 and Ch.30

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30.13.15

S^{m(1)}_{n}\left(\xi_{0},\gamma\right)=0.

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Symbols:: $S^{\NVar{m}(\NVar{j})}_{\NVar{n}}\left(\NVar{z},\NVar{\gamma}\right)$ : radial spheroidal wave function, $m$ : nonnegative integer, $n\geq m$ : integer degree, $\xi$ : prolate spheroidal coordinate and $\gamma^{2}$ : real parameter
Permalink:: http://dlmf.nist.gov/30.13.E15
Encodings:: pMML, png, TeX
See also:: Annotations for §30.13(v), §30.13 and Ch.30

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24: 31.17 Physical Applications

… ►More applications—including those of generalized spheroidal wave functions and confluent Heun functions in mathematical physics, astrophysics, and the two-center problem in molecular quantum mechanics—can be found in Leaver (1986) and Slavyanov and Lay (2000, Chapter 4). …

25: Bibliography S

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D. Slepian and H. O. Pollak (1961) Prolate spheroidal wave functions, Fourier analysis and uncertainty. I. Bell System Tech. J. 40, pp. 43–63.

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External Links:: MathReview (I. Marx), ZentralBlatt
Referenced by:: §30.15(v).
Encodings:: BibTeX

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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.

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External Links:: ISSN 0005-8580, MathReview (J. Meixner), ZentralBlatt
Referenced by:: §30.12.
Encodings:: BibTeX

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J. A. Stratton, P. M. Morse, L. J. Chu, and R. A. Hutner (1941) Elliptic Cylinder and Spheroidal Wave Functions, Including Tables of Separation Constants and Coefficients. John Wiley and Sons, Inc., New York.

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External Links:: MathReview (H. Bateman), ZentralBlatt
Referenced by:: §28.1, 7th item, Notations S, Notations S.
Encodings:: BibTeX

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J. A. Stratton, P. M. Morse, L. J. Chu, J. D. C. Little, and F. J. Corbató (1956) Spheroidal Wave Functions: Including Tables of Separation Constants and Coefficients. Technology Press of M. I. T. and John Wiley & Sons, Inc., New York.

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External Links:: ISBN 0262190028, 0262692910, MathReview (A. Erdélyi), ZentralBlatt
Referenced by:: 1st item, Ch.30.
Encodings:: BibTeX

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26: Bibliography E

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S. P. EraŠevskaja, E. A. Ivanov, A. A. Pal’cev, and N. D. Sokolova (1973) Tablicy sferoidal’nyh volnovyh funkcii i ih pervyh proizvodnyh. Tom I. Izdat. “Nauka i Tehnika”, Minsk (Russian).

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Notes:: Translated title: Tables of Spheroidal Wave Functions and Their First Derivatives.
External Links:: MathReview, ZentralBlatt
Referenced by:: 4th item.
Encodings:: BibTeX

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S. P. EraŠevskaja, E. A. Ivanov, A. A. Pal’cev, and N. D. Sokolova (1976) Tablicy sferoidal’nyh volnovyh funkcii iih pervyh proizvodnyh. Tom II. Izdat. “Nauka i Tehnika”, Minsk (Russian).

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Notes:: Edited by V. I. Krylov. Translated title: Tables of Spheroidal Wave Functions and Their First Derivatives.
External Links:: MathReview
Referenced by:: 4th item.
Encodings:: BibTeX

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27: Bibliography F

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P. Falloon (2001) Theory and Computation of Spheroidal Harmonics with General Arguments. Master’s Thesis, The University of Western Australia, Department of Physics.

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Notes:: Contains Mathematica package for spheroidal wave functions of complex arguments with complex parameters.
External Links:: FullText
Referenced by:: §30.12, 1st item, 2nd item.
Encodings:: BibTeX

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C. Flammer (1957) Spheroidal Wave Functions. Stanford University Press, Stanford, CA.

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External Links:: MathReview (J. C. P. Miller), ZentralBlatt
Referenced by:: §30.1, §30.10, 2nd item, Ch.30.
Encodings:: BibTeX

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28: Bibliography B

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T. A. Beu and R. I. Câmpeanu (1983a) Prolate angular spheroidal wave functions. Comput. Phys. Comm. 30 (2), pp. 187–192.

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External Links:: Document, Code
Referenced by:: 1st item.
Encodings:: BibTeX

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T. A. Beu and R. I. Câmpeanu (1983b) Prolate radial spheroidal wave functions. Comput. Phys. Comm. 30 (2), pp. 177–185.

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External Links:: Document, Code
Referenced by:: 1st item.
Encodings:: BibTeX

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C. J. Bouwkamp (1947) On spheroidal wave functions of order zero. J. Math. Phys. Mass. Inst. Tech. 26, pp. 79–92.

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External Links:: ISSN 0097-1421, MathReview (M. J. O. Strutt), ZentralBlatt
Referenced by:: §30.16(i).
Encodings:: BibTeX

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29: Bibliography M

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J. W. Miles (1975) Asymptotic approximations for prolate spheroidal wave functions. Studies in Appl. Math. 54 (4), pp. 315–349.

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External Links:: MathReview (M. L. Mehta), ZentralBlatt
Referenced by:: §30.9(i).
Encodings:: BibTeX

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H. J. W. Müller (1962) Asymptotic expansions of oblate spheroidal wave functions and their characteristic numbers. J. Reine Angew. Math. 211, pp. 33–47.

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External Links:: MathReview (J. Meixner), ZentralBlatt
Referenced by:: §30.9(ii), §30.9(ii).
Encodings:: BibTeX

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H. J. W. Müller (1963) Asymptotic expansions of prolate spheroidal wave functions and their characteristic numbers. J. Reine Angew. Math. 212, pp. 26–48.

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