spheroidal harmonics
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1: 14.30 Spherical and Spheroidal Harmonics
§14.30 Spherical and Spheroidal Harmonics
… ► and () are often referred to as the prolate spheroidal harmonics of the first and second kinds, respectively. and () are known as oblate spheroidal harmonics of the first and second kinds, respectively. Segura and Gil (1999) introduced the scaled oblate spheroidal harmonics and which are real when and . …2: Bibliography F
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Theory and Computation of Spheroidal Harmonics with General Arguments.
Master’s Thesis, The University of Western Australia, Department of Physics.
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3: Bibliography G
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A code to evaluate prolate and oblate spheroidal harmonics.
Comput. Phys. Comm. 108 (2-3), pp. 267–278.
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4: Bibliography L
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Computations of spheroidal harmonics with complex arguments: A review with an algorithm.
Phys. Rev. E 58 (5), pp. 6792–6806.
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5: Bibliography M
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Spherical Harmonics. An Elementary Treatise on Harmonic Functions with Applications.
3rd edition, International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford.
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New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems.
J. Math. Phys. 54 (10), pp. Paper 102102, 12 pp..
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Catastrophe optics of spheroidal drops and generalized rainbows.
J. Quantit. Spec. and Rad. Trans. 63, pp. 341–351.
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On the evaluation of Bessel functions.
Appl. Comput. Harmon. Anal. 1 (1), pp. 116–135.
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Asymptotic approximations for prolate spheroidal wave functions.
Studies in Appl. Math. 54 (4), pp. 315–349.
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6: Bibliography H
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Tables of Radial Spheroidal Wave Functions, Vols. 1-3, Prolate, ; Vols. 4-6, Oblate,
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Technical report
Naval Research Laboratory, Washington, D.C..
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The Theory of Spherical and Ellipsoidal Harmonics.
Cambridge University Press, London-New York.
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Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains.
Translations of Mathematical Monographs, Vol. 6, American Mathematical Society, Providence, RI.
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The eigenvalues of the angular spheroidal wave equation.
Stud. Appl. Math. 66 (3), pp. 217–240.
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7: Bibliography V
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Calculation of spheroidal wave functions.
J. Acoust. Soc. Amer. 51, pp. 414–416.
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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..
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Mathieu and Spheroidal Wave Functions: Fortran Programs for their Accurate Calculation
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Expansion of vacuum magnetic fields in toroidal harmonics.
Comput. Phys. Comm. 81 (1-2), pp. 74–90.
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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8: Bibliography
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Asymptotic expansions of spheroidal wave functions.
J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.
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SPHEREPACK 2.0: A Model Development Facility.
NCAR Technical Note
Technical Report TN-436-STR, National Center for Atmospheric Research.
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A harmonic mean inequality for the gamma function.
J. Comput. Appl. Math. 87 (2), pp. 195–198.
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9: Bibliography B
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Prolate angular spheroidal wave functions.
Comput. Phys. Comm. 30 (2), pp. 187–192.
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Prolate radial spheroidal wave functions.
Comput. Phys. Comm. 30 (2), pp. 177–185.
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On spheroidal wave functions of order zero.
J. Math. Phys. Mass. Inst. Tech. 26, pp. 79–92.
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Associated Legendre polynomials, ordinary and modified spherical harmonics.
Comput. Phys. Comm. 5 (5), pp. 390–394.
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Two cold atoms in a harmonic trap.
Found. Phys. 28 (4), pp. 549–559.
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