kernel%20functions
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1: 10.75 Tables
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The main tables in Abramowitz and Stegun (1964, Chapter 9) give to 15D, , , , to 10D, to 8D, ; , , , 8D; , , , , 5D or 5S; , , , , 10S; modulus and phase functions , , , , 8D.
Abramowitz and Stegun (1964, Chapter 9) tabulates , , , , , , 9–10D; , , , , 9D; modulus and phase functions , , , , , , 6D; , , , , , , 5D.
Zhang and Jin (1996, p. 322) tabulates , , , , , , , , , 7S.
Zhang and Jin (1996, p. 323) tabulates the first real zeros of , , , , , , , , 8D.
2: 10.73 Physical Applications
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►See Krivoshlykov (1994, Chapter 2, §2.2.10; Chapter 5, §5.2.2), Kapany and Burke (1972, Chapters 4–6; Chapter 7, §A.1), and Slater (1942, Chapter 4, §§20, 25).
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§10.73(iii) Kelvin Functions
►The analysis of the current distribution in circular conductors leads to the Kelvin functions , , , and . … ►§10.73(iv) Bickley Functions
…3: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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Szegő Type Asymptotics for the Reproducing Kernel in Spaces of Full-Plane Weighted Polynomials.
Comm. Math. Phys. 398 (3), pp. 1291–1348.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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4: 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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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Exact error terms in the asymptotic expansion of a class of integral transforms. I. Oscillatory kernels.
SIAM J. Math. Anal. 11 (5), pp. 828–841.
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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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