for prolate spheroids
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1—10 of 15 matching pages
1: Bibliography X
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Prolate spheroidal wavefunctions, quadrature and interpolation.
Inverse Problems 17 (4), pp. 805–838.
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2: 30.13 Wave Equation in Prolate Spheroidal Coordinates
§30.13 Wave Equation in Prolate Spheroidal Coordinates
►§30.13(i) Prolate Spheroidal Coordinates
… ►§30.13(ii) Metric Coefficients
… ►§30.13(iii) Laplacian
… ►3: Bibliography V
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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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Accurate calculation of prolate spheroidal radial functions of the first kind and their first derivatives.
Quart. Appl. Math. 60 (3), pp. 589–599.
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Improved calculation of prolate spheroidal radial functions of the second kind and their first derivatives.
Quart. Appl. Math. 62 (3), pp. 493–507.
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4: 30.9 Asymptotic Approximations and Expansions
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§30.9(i) Prolate Spheroidal Wave Functions
…5: 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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6: 30.1 Special Notation
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7: 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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8: Bibliography S
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Prolate spheroidal wave functions, Fourier analysis and uncertainty. I.
Bell System Tech. J. 40, pp. 43–63.
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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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9: 14.30 Spherical and Spheroidal Harmonics
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and () are often referred to as the prolate spheroidal harmonics of the first and second kinds, respectively.
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