wave%20functions
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1—10 of 19 matching pages
1: 10.73 Physical Applications
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►This equation governs problems in acoustic and electromagnetic wave propagation.
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►More recently, Bessel functions appear in the inverse problem in wave propagation, with applications in medicine, astronomy, and acoustic imaging.
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§10.73(ii) Spherical Bessel Functions
… ►In quantum mechanics the spherical Bessel functions arise in the solution of the Schrödinger wave equation for a particle in a central potential. …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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Spheroidal Wave Functions.
Stanford University Press, Stanford, CA.
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Diffraction of radio waves around the earth’s surface.
Acad. Sci. USSR. J. Phys. 9, pp. 255–266.
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Numerical treatment of Coulomb wave functions.
Rev. Mod. Phys. 27 (4), pp. 399–411.
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3: Bibliography V
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Calculation of spheroidal wave functions.
J. Acoust. Soc. Amer. 51, pp. 414–416.
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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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A Mathieu equation for ships rolling among waves. I, II.
Norske Vid. Selsk. Forh., Trondheim 22 (25–26), pp. 113–123.
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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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4: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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Scattering theory of waves and particles.
Dover Publications, Inc., Mineola, NY.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations.
Institute of Physics Publishing, Bristol.
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5: 30.9 Asymptotic Approximations and Expansions
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§30.9(i) Prolate Spheroidal Wave Functions
… ►§30.9(ii) Oblate Spheroidal Wave Functions
… ►§30.9(iii) Other Approximations and Expansions
… ►The asymptotic behavior of and as is given in Erdélyi et al. (1955, p. 151). …6: Bibliography
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Evaluation of Coulomb wave functions along the transition line.
Physical Rev. (2) 96, pp. 77–79.
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Asymptotic expansions of spheroidal wave functions.
J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.
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Regular and irregular Coulomb wave functions expressed in terms of Bessel-Clifford functions.
J. Math. Physics 33, pp. 111–116.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Perturbation solutions of the ellipsoidal wave equation.
Quart. J. Math. Oxford Ser. (2) 7, pp. 161–174.
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7: Bibliography B
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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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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The determination of phases and amplitudes of wave functions.
Proc. Phys. Soc. 81 (3), pp. 442–452.
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8: Bibliography M
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Precise Coulomb wave functions for a wide range of complex , and
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Computer Physics Communications 176 (3), pp. 232–249.
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Asymptotic approximations for prolate spheroidal wave functions.
Studies in Appl. Math. 54 (4), pp. 315–349.
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Asymptotic expansions of oblate spheroidal wave functions and their characteristic numbers.
J. Reine Angew. Math. 211, pp. 33–47.
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Asymptotic expansions of ellipsoidal wave functions in terms of Hermite functions.
Math. Nachr. 32, pp. 49–62.
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On asymptotic expansions of ellipsoidal wave functions.
Math. Nachr. 32, pp. 157–172.
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9: Software Index
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►‘✓’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support.
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►In the list below we identify four main sources of software for computing special functions.
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Commercial Software.
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►The following are web-based software repositories with significant holdings in the area of special functions.
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Open Source | With Book | Commercial | |||||||||||||||||||||||
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20 Theta Functions | |||||||||||||||||||||||||
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Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.
10: Bibliography S
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The determination of phases of wave functions.
Proc. Phys. Soc. 79 (6), pp. 1296–1297.
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FGH, a code for the calculation of Coulomb radial wave functions from series expansions.
Comput. Phys. Comm. 146 (2), pp. 250–253.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Integral equations and relations for Lamé functions and ellipsoidal wave functions.
Proc. Cambridge Philos. Soc. 64, pp. 113–126.
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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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