connection%20with%20spheroidal%20wave%0Afunctions
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21—30 of 751 matching pages
21: Bibliography I
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The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of and of Bessel functions of any real order
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Linear Algebra Appl. 194, pp. 35–70.
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The zeros of regular Coulomb wave functions and of their derivatives.
Math. Comp. 29, pp. 878–887.
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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Connection formulae for the fourth Painlevé transcendent; Clarkson-McLeod solution.
J. Phys. A 31 (17), pp. 4073–4113.
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22: 31.18 Methods of Computation
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►Subsequently, the coefficients in the necessary connection formulas can be calculated numerically by matching the values of solutions and their derivatives at suitably chosen values of ; see Laĭ (1994) and Lay et al. (1998).
…The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 28–30.
23: Gergő Nemes
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►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
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24: Wolter Groenevelt
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►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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25: Bibliography C
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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A connection formula for the second Painlevé transcendent.
Arch. Rational Mech. Anal. 103 (2), pp. 97–138.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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An approximation connected with
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Proc. Edinburgh Math. Soc. (2) 3, pp. 201–206.
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26: Bibliography O
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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Connection formulas for second-order differential equations with multiple turning points.
SIAM J. Math. Anal. 8 (1), pp. 127–154.
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Connection formulas for second-order differential equations having an arbitrary number of turning points of arbitrary multiplicities.
SIAM J. Math. Anal. 8 (4), pp. 673–700.
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General connection formulae for Liouville-Green approximations in the complex plane.
Philos. Trans. Roy. Soc. London Ser. A 289, pp. 501–548.
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A closed form solution of the -wave Bethe-Goldstone equation with an infinite repulsive core.
J. Math. Phys. 27 (4), pp. 1154–1158.
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27: 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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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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Mathieu and Spheroidal Wave Functions: Fortran Programs for their Accurate Calculation
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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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28: Bibliography W
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Surface Waves.
In Handbuch der Physik, Vol. 9, Part 3,
pp. 446–778.
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On the central connection problem for the double confluent Heun equation.
Math. Nachr. 195, pp. 267–276.
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On the connection formulas of the fourth Painlevé transcendent.
Anal. Appl. (Singap.) 7 (4), pp. 419–448.
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On the connection formulas of the third Painlevé transcendent.
Discrete Contin. Dyn. Syst. 23 (1-2), pp. 541–560.
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29: 36.14 Other Physical Applications
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►Diffraction catastrophes describe the (linear) wave amplitudes that smooth the geometrical caustic singularities and decorate them with interference patterns.
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►Diffraction catastrophes describe the connection between ray optics and wave optics.
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►Diffraction catastrophes describe the “semiclassical” connections between classical orbits and quantum wavefunctions, for integrable (non-chaotic) systems.
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30: 6.19 Tables
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Abramowitz and Stegun (1964, Chapter 5) includes , , , , ; , , , , ; , , , , ; , , , , ; , , . Accuracy varies but is within the range 8S–11S.
Zhang and Jin (1996, pp. 652, 689) includes , , , 8D; , , , 8S.
Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of , , , 6D; , , , 6D; , , , 6D.
Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of , , , 8S.