Computation of radial prolate spheroidal wave functions using Jaffe's series expansions

Computational Mathematics and Mathematical Physics

Volumn 43, Issue 9, 2003, Pages 1299-1309

  Voshchinnikov, N V ^a   Farafonov, V G ^b  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^b SAINT PETERSBURG STATE UNIVERSITY OF AEROSPACE INSTRUMENTATION   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746167207     PISSN: 09655425     EISSN: 15556662     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. Meixner, J. and Schafke, F.W., Mathieusche Funktionen und Spharoidfunktionen, mit Anwendungen auf physikalische und technische Probleme, Berlin: Springer-Verlag, 1954.
2. Komarov, I.V., Ponomarev, L.N., and Slavyanov, S.Yu., Sferoitlal'nye i kulonovskie sferoidal'nye funktsii (Spheroidal and Coulomb Spheroidal Functions), Moscow: Nauka, 1976.
3. Flammer, C., Spheroidal Wave Functions, Stanford: Stanford Univ. Press, 1957.
4. Translated under the title Tablitsy volnovykh sferoidal'nykh funktsii, Moscow: Vychisl. Tscntr Akad. Nauk SSSR, 1962.
5. Hanish, S., Baicr, R.V., van Buren, A.Z., and King, B.J., Tables of Radial Spheroidal Wave Functions, U.S. Naval Res. Lab. Rep., Washington, D.C., 1971, nos. 7088-7090.
6. Erashevskaya, S.P., Ivanov, E.A., Pal'tsev, A.A., and Sokolova, N.D., Tablitsy sferoidal'nykh volnovykh funktsii i ikh pervykh proizvodnykh (Tables of Spheroidal Wave Functions and Their First Derivatives), Minsk: Nauka i Tekhnika, 1973, vol. 1.
7. Erashevskaya, S.P., Ivanov, E.A., Pal'tsev, A.A., and Sokolova, N.D., Tablitsy sferoidal'nykh volnovykh funktsii i ikh pervykh proizvodnykh (Tables of Spheroidal Wave Functions and Their First Derivatives), Minsk: Nauka i Tekhnika, 1976, vol. 2.
8. Abramov, A.A., Dyshko, A.D., Konyukhoya, N.B., Pak, T.V., and Pariiskii, B.S., Computation of Prolate Spheroidal Functions by Solving the Corresponding Differential Equations, Zh. Vychisl. Mat. Mat. Fiz., 1984, vol. 24, no. 1, pp. 3-18.
9. Abramov, A.A., Dyshko, A.D., Konyukhova, N.B., and Levitina, T.V., Computation of Radial Wave Functions for Spheroids and Triaxial Ellipsoids by a Modified Method of Phase Functions, Zh. Vychisl. Mat. Mat. Fiz., 1991, vol. 31, no. 2, pp. 212-234.
10. Lay, W. and Slavyanov, S.Yu., The Central Two-Point Connection Problem for the Heun Class of ODE, J. Phys. A: Math. Gen., 1998, vol. 31, pp. 8521-8531.
11. Voshchinnikov, N.V. and Farafonov, V.G., Optical Properties of Spheroidal Particles, Astrophys. Space Sci., 1993, vol. 204, pp. 19-86.
12. Mishchenko, M.I., Wiscombe, W.J., Hovenier, J.W., and Travis, L.D., Overview of Scattering by Nonspherical Particles, in Light Scattering by Nonspherical Particles, Mishchenko, M.I. et al., Eds., San Francisco: Academic, 2000, pp. 30-60.