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21—30 of 122 matching pages
21: 29.18 Mathematical Applications
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§29.18(iii) Spherical and Ellipsoidal Harmonics
…22: 34.3 Basic Properties: Symbol
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§34.3(vii) Relations to Legendre Polynomials and Spherical Harmonics
βΊFor the polynomials see §18.3, and for the function see §14.30. … βΊ
34.3.20
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34.3.22
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23: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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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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24: 25.16 Mathematical Applications
25: 36 Integrals with Coalescing Saddles
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26: GergΕ Nemes
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βΊAs 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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27: Wolter Groenevelt
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βΊAs 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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28: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann.
Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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The constrained quantum mechanical harmonic oscillator.
Proc. Cambridge Philos. Soc. 62, pp. 277–286.
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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29: 33.24 Tables
30: 12.17 Physical Applications
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βΊDean (1966) describes the role of PCFs in quantum mechanical systems closely related to the one-dimensional harmonic oscillator.
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βΊFor this topic and other boundary-value problems see Boyd (1973), Hillion (1997), Magnus (1941), Morse and Feshbach (1953a, b), Müller (1988), Ott (1985), Rice (1954), and Shanmugam (1978).
βΊLastly, parabolic cylinder functions arise in the description of ultra cold atoms in harmonic trapping potentials; see Busch et al. (1998) and Edwards et al. (1999).