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21—30 of 172 matching pages
21: 18.1 Notation
22: Bibliography M
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A -analog of the summation theorem for hypergeometric series well-poised in
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Adv. in Math. 57 (1), pp. 14–33.
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A -analog of hypergeometric series well-poised in and invariant -functions.
Adv. in Math. 58 (1), pp. 1–60.
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A -analog of the Gauss summation theorem for hypergeometric series in
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Adv. in Math. 72 (1), pp. 59–131.
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A -analog of a Whipple’s transformation for hypergeometric series in
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Adv. Math. 108 (1), pp. 1–76.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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23: 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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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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A combinatorial interpretation of the Seidel generation of Genocchi numbers.
Ann. Discrete Math. 6, pp. 77–87.
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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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24: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation.
Adv. Quantum Chem. 72, pp. 95–127.
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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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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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25: 17.17 Physical Applications
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βΊThey were given this name because they play a role in quantum physics analogous to the role of Lie groups and special functions in classical mechanics.
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26: 25.17 Physical Applications
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βΊAnalogies exist between the distribution of the zeros of on the critical line and of semiclassical quantum eigenvalues.
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27: 18.19 Hahn Class: Definitions
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βΊThe Hahn class consists of four discrete families (Hahn, Krawtchouk, Meixner, and Charlier) and two continuous families (continuous Hahn and Meixner–Pollaczek).
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Hahn class (or linear lattice class). These are OP’s where the role of is played by or or (see §18.1(i) for the definition of these operators). The Hahn class consists of four discrete and two continuous families.
Wilson class (or quadratic lattice class). These are OP’s ( of degree in , quadratic in ) where the role of the differentiation operator is played by or or . The Wilson class consists of two discrete and two continuous families.
28: 24.19 Methods of Computation
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29: 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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On the connection formulas of the third Painlevé transcendent.
Discrete Contin. Dyn. Syst. 23 (1-2), pp. 541–560.
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30: 8 Incomplete Gamma and Related
Functions
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