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1: 26.9 Integer Partitions: Restricted Number and Part Size
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Table 26.9.1: Partitions .
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►Equations (26.9.2)–(26.9.3) are examples of closed forms that can be computed explicitly for any positive integer .
See Andrews (1976, p. 81).
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0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
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7 | 0 | 1 | 4 | 8 | 11 | 13 | 14 | 15 | 15 | 15 | 15 |
8 | 0 | 1 | 5 | 10 | 15 | 18 | 20 | 21 | 22 | 22 | 22 |
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2: 22.17 Moduli Outside the Interval [0,1]
3: 26.6 Other Lattice Path Numbers
4: 4.5 Inequalities
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►For more inequalities involving the exponential function see Mitrinović (1964, pp. 73–77), Mitrinović (1970, pp. 266–271), and Bullen (1998, pp. 81–83).
5: Bibliography V
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Integrating products of Bessel functions with an additional exponential or rational factor.
Comput. Phys. Comm. 178 (8), pp. 578–590.
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Expansion of vacuum magnetic fields in toroidal harmonics.
Comput. Phys. Comm. 81 (1-2), pp. 74–90.
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Asymptotic expansion of the generalized hypergeometric function as for
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Anal. Appl. (Singap.) 21 (2), pp. 535–545.
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On the rational solutions of the second Painlevé equation.
Differ. Uravn. 1 (1), pp. 79–81 (Russian).
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6: Bibliography L
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Inequalities for Bessel functions.
J. Comput. Appl. Math. 15 (1), pp. 75–81.
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Some differential equations and associated integral equations.
Quart. J. Math. (Oxford) 5, pp. 81–97.
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Monotonicity of the differences of zeros of Bessel functions as a function of order.
Proc. Amer. Math. Soc. 15 (1), pp. 91–96.
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Numerical Evaluation of Special Functions.
In Mathematics of Computation 1943–1993: A Half-Century of
Computational Mathematics (Vancouver, BC, 1993),
Proc. Sympos. Appl. Math., Vol. 48, pp. 79–125.
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Miniaturized tables of Bessel functions. III.
Math. Comp. 26 (117), pp. 237–240 and A14–B5.
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7: 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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Unsteady lifting-line theory as a singular-perturbation problem.
J. Fluid Mech 153, pp. 59–81.
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Sturm-Liouville Theory.
Birkhäuser Verlag, Basel.
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A primer on Bernoulli numbers and polynomials.
Math. Mag. 81 (3), pp. 178–190.
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Singular Continuous Spectrum for a Class of Almost Periodic Jacobi Matrices.
Bulletin of the American Mathematical Society 6 (1), pp. 81–85.
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8: Bibliography Z
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Remark on “Algorithm 916: computing the Faddeyeva and Voigt functions”: efficiency improvements and Fortran translation.
ACM Trans. Math. Softw. 42 (3), pp. 26:1–26:9.
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Algorithm 985: Simple, Efficient, and Relatively Accurate Approximation for the Evaluation of the Faddeyeva Function.
ACM Trans. Math. Softw. 44 (2), pp. 22:1–22:9.
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Su un integrale definito del prodotto di due funzioni di Struve.
Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 112 (1-2), pp. 63–81 (Italian).
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A note on the -method approximations for the Bessel functions and
.
Comput. Math. Appl. 31 (9), pp. 63–70.
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Chebyshev series approximations for the Bessel function of complex argument.
Appl. Math. Comput. 88 (2-3), pp. 275–286.
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9: Bibliography H
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Computation of certain integrals that contain a probability function.
Bul. Akad. Štiince RSS Moldoven 1968 (2), pp. 81–104. (errata insert) (Russian).
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Expansions for the probability function in series of Čebyšev polynomials and Bessel functions.
Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 77–80, 96 (Russian).
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Integrals that contain a probability function of complicated arguments.
Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 80–84, 96 (Russian).
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Lamé polynomials of large order.
SIAM J. Math. Anal. 8 (5), pp. 800–842.
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High frequency solutions of the delta wing equations.
Proc. Roy. Soc. Edinburgh Sect. A 81 (3-4), pp. 299–316.
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10: Tom H. Koornwinder
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►Koornwinder has published numerous papers on special functions, harmonic analysis, Lie groups, quantum groups, computer algebra, and their interrelations, including an interpretation of Askey–Wilson polynomials on quantum SU(2), and a five-parameter extension (the Macdonald–Koornwinder polynomials) of Macdonald’s polynomials for root systems BC.
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