Mehler%E2%80%93Fock%20transformation
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21: 32.8 Rational Solutions
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– possess hierarchies of rational solutions for special values of the parameters which are generated from “seed solutions” using the Bäcklund transformations and often can be expressed in the form of determinants.
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►Rational solutions of exist for and are generated using the seed solution and the Bäcklund transformations (32.7.1) and (32.7.2).
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32.8.3
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32.8.4
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22: 8.23 Statistical Applications
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►In queueing theory the Erlang loss function is used, which can be expressed in terms of the reciprocal of ; see Jagerman (1974) and Cooper (1981, pp. 80, 316–319).
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23: 26.13 Permutations: Cycle Notation
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24: Bibliography J
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A note on sampling expansion for a transform with parabolic cylinder kernel.
Inform. Sci. 26 (2), pp. 155–158.
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Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent.
Phys. D 1 (1), pp. 80–158.
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Fast Hankel transforms.
Geophysical Prospecting 27 (4), pp. 876–901.
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Asymptotic behavior of the continued fraction coefficients of a class of Stieltjes transforms including the Binet function.
In Orthogonal functions, moment theory, and continued fractions
(Campinas, 1996),
Lecture Notes in Pure and Appl. Math., Vol. 199, pp. 257–274.
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Modifications of Coulombic interactions by polarizable atoms.
Math. Proc. Cambridge Philos. Soc. 80 (3), pp. 535–539.
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25: 26.6 Other Lattice Path Numbers
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Table 26.6.1: Delannoy numbers .
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10 | 1 | 21 | 221 | 1561 | 8361 | 36365 | 1 34245 | 4 33905 | 12 56465 | 33 17445 | 80 97453 |
26: Bibliography P
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A Kummer-type transformation for a hypergeometric function.
J. Comput. Appl. Math. 173 (2), pp. 379–382.
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Bounds for ratios of modified Bessel functions.
Integral Transform. Spec. Funct. 9 (4), pp. 293–298.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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Fourier Series and Integral Transforms.
Cambridge University Press, Cambridge.
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Stacking models of vesicles and compact clusters.
J. Statist. Phys. 80 (3–4), pp. 755–779.
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27: 36.5 Stokes Sets
28: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Electromagnetic Diffraction and Propagation Problems.
International Series of Monographs on Electromagnetic Waves,
Vol. 1, Pergamon Press, Oxford.
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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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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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29: 9.1 Special Notation
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►Other notations that have been used are as follows: and for and (Jeffreys (1928), later changed to and ); , (Fock (1945)); (Szegő (1967, §1.81)); , (Tumarkin (1959)).
30: 10.31 Power Series
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