oblate spheroidal
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1: 30.14 Wave Equation in Oblate Spheroidal Coordinates
§30.14 Wave Equation in Oblate Spheroidal Coordinates
►§30.14(i) Oblate Spheroidal Coordinates
… ►§30.14(ii) Metric Coefficients
… ►§30.14(iii) Laplacian
… ►2: 30.9 Asymptotic Approximations and Expansions
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§30.9(ii) Oblate Spheroidal Wave Functions
…3: 30.2 Differential Equations
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►In applications involving prolate spheroidal coordinates is positive, in applications involving oblate spheroidal coordinates is negative; see §§30.13, 30.14.
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4: 30.1 Special Notation
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5: Bibliography V
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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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Tables of Angular Spheroidal Wave Functions, Vol. 1, Prolate, ; Vol. 2, Oblate, m=0.
Naval Res. Lab. Reports, Washington, D.C..
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6: Bibliography J
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Derivation of Green-type, transitional and uniform asymptotic expansions from differential equations. V. Angular oblate spheroidal wavefunctions and for large
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Proc. Roy. Soc. London Ser. A 321, pp. 545–555.
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7: Bibliography D
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Uniform asymptotic expansions for oblate spheroidal functions I: Positive separation parameter
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Proc. Roy. Soc. Edinburgh Sect. A 121 (3-4), pp. 303–320.
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Uniform asymptotic expansions for oblate spheroidal functions II: Negative separation parameter
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Proc. Roy. Soc. Edinburgh Sect. A 125 (4), pp. 719–737.
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8: 14.30 Spherical and Spheroidal Harmonics
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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 .
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9: 30.4 Functions of the First Kind
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►When
is the prolate angular spheroidal wave function, and when
is the oblate angular spheroidal wave function.
If , reduces to the Ferrers function :
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10: 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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