Improving the convergence in an expansion of spheroidal wave functions
Authors:
J. Meixner and C. P. Wells
Journal:
Quart. Appl. Math. 17 (1959), 263-269
MSC:
Primary 65.00; Secondary 33.00
DOI:
https://doi.org/10.1090/qam/105793
MathSciNet review:
105793
Full-text PDF Free Access
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Additional Information
H. Myers, Radiation patterns of the prolate spheroidal antenna, Trans. I. R. E. AP-4, 58–64 (1956)
C. P. Wells, The prolate spheroidal antenna: Current and impedance, Trans. I. R. E. AP-6, 125–128 (1958)
- Josef Meixner and Friedrich Wilhelm Schäfke, Mathieusche Funktionen und Sphäroidfunktionen mit Anwendungen auf physikalische und technische Probleme, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band LXXI, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1954 (German). MR 0066500
- Carson Flammer, Spheroidal wave functions, Stanford University Press, Stanford, California, 1957. MR 0089520
J. Meixner and W. Kloepfer, Theorie der ebenen Ringspalt-antenne, Z. Physik 3, 171–178 (1951)
- G. N. Watson, Notes on Generating Functions of Polynomials: (3) Polynomials of Legendre and Gegenbauer, J. London Math. Soc. 8 (1933), no. 4, 289–292. MR 1573972, DOI https://doi.org/10.1112/jlms/s1-8.4.289
K. Knopp, Theory and application of infinite series, Blackie and Sons, London, 1928
G. Szegö, Entwicklungen der Legendreschen Funktionen, Proc. Lond. Math. Soc. 36, 427–450 (1933)
A. Erdélyi et al., Higher transcendental functions vol. 2, McGraw-Hill, New York, 1953
H. Myers, Radiation patterns of the prolate spheroidal antenna, Trans. I. R. E. AP-4, 58–64 (1956)
C. P. Wells, The prolate spheroidal antenna: Current and impedance, Trans. I. R. E. AP-6, 125–128 (1958)
J. Meixner and F. W. Schafke, Mathieusche Funktionen und Spharoidfunktionen, Springer Verlag, Berlin, 1954
C. Flammer, Spheroidal wave functions, Standord University Press, Stanford, Calif., 1957
J. Meixner and W. Kloepfer, Theorie der ebenen Ringspalt-antenne, Z. Physik 3, 171–178 (1951)
G. N. Watson, Notes on generating functions of polynomials, III, Polynomials of Legendre and Gegenbauer, J. Lond. Math. Soc. 8, 289–292 (1933)
K. Knopp, Theory and application of infinite series, Blackie and Sons, London, 1928
G. Szegö, Entwicklungen der Legendreschen Funktionen, Proc. Lond. Math. Soc. 36, 427–450 (1933)
A. Erdélyi et al., Higher transcendental functions vol. 2, McGraw-Hill, New York, 1953
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Article copyright:
© Copyright 1959
American Mathematical Society
