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1: 26.2 Basic Definitions
2: Bibliography I
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βΊ
The zeros of regular Coulomb wave functions and of their derivatives.
Math. Comp. 29, pp. 878–887.
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An integral which occurs in statistics.
Proceedings of the Cambridge Philosophical Society 29, pp. 271–276.
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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βΊ
A Classical Introduction to Modern Number Theory.
2nd edition, Springer-Verlag, New York.
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3: 27.2 Functions
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βΊwhere are the distinct prime factors of , each exponent is positive, and is the number of distinct primes dividing .
…Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes.
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βΊ(See Gauss (1863, Band II, pp. 437–477) and Legendre (1808, p. 394).)
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βΊ
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βΊ
§27.2(ii) Tables
…4: 26.12 Plane Partitions
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βΊ
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βΊThen the number of plane partitions in is
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βΊThe number of symmetric plane partitions in is
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βΊThe number of cyclically symmetric plane partitions in is
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βΊThe number of descending plane partitions in is
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5: 26.9 Integer Partitions: Restricted Number and Part Size
§26.9 Integer Partitions: Restricted Number and Part Size
… βΊ denotes the number of partitions of into at most parts. See Table 26.9.1. … βΊis the Gaussian polynomial (or -binomial coefficient); see also §§17.2(i)–17.2(ii). …6: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
§26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
βΊ§26.4(i) Definitions
βΊ is the number of ways of placing distinct objects into labeled boxes so that there are objects in the th box. … βΊ§26.4(ii) Generating Function
… βΊ§26.4(iii) Recurrence Relation
…7: Bibliography M
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βΊ
Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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βΊ
The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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βΊ
Calculation of the complete elliptic integrals with complex modulus.
Numer. Math. 29 (2), pp. 233–236.
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βΊ
Stirling numbers of the second kind.
Duke Math. J. 25 (1), pp. 29–43.
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Rational solutions of the second and the fourth Painlevé equations.
Funkcial. Ekvac. 28 (1), pp. 1–32.
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8: Bibliography
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Asymptotic expansions of spheroidal wave functions.
J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.
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Theory of Incomplete Cylindrical Functions and Their Applications.
Springer-Verlag, Berlin.
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Study of nuclear structure by electromagnetic excitation with accelerated ions.
Rev. Mod. Phys. 28, pp. 432–542.
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Computation of modified Bessel functions and their ratios.
Math. Comp. 28 (125), pp. 239–251.
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βΊ
Normal forms of functions in the neighborhood of degenerate critical points.
Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).
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9: Bibliography L
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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List of Prime Numbers from 1 to 10,006,721.
Publ. No. 165, Carnegie Institution of Washington, Washington, D.C..
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Eine Verallgemeinerung der Sphäroidfunktionen.
Arch. Math. 11, pp. 29–39.
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βΊ
Lie algebraic approaches to classical partition identities.
Adv. in Math. 29 (1), pp. 15–59.
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βΊ
New recursion relation for the Clebsch-Gordan coefficients.
Phys. Rev. (2) 110 (4), pp. 815–816.
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10: Bibliography S
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βΊ
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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βΊ
Recursive evaluation of - and - coefficients.
Comput. Phys. Comm. 11 (2), pp. 269–278.
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βΊ
Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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βΊ
The elliptical microstrip antenna with circular polarization.
IEEE Trans. Antennas and Propagation 29 (1), pp. 90–94.
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βΊ
Sturm oscillation and comparison theorems.
In Sturm-Liouville theory,
pp. 29–43.
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