Bailey%20chain
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1: 17.12 Bailey Pairs
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Bailey Transform
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… ►When (17.12.5) is iterated the resulting infinite sequence of Bailey pairs is called a Bailey Chain. … ►The Bailey pair and Bailey chain concepts have been extended considerably. …2: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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Nonlinear chains and Painlevé equations.
Phys. D 73 (4), pp. 335–351.
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A trinomial analogue of Bailey’s lemma and superconformal invariance.
Comm. Math. Phys. 192 (2), pp. 245–260.
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Umbral calculus, Bailey chains, and pentagonal number theorems.
J. Combin. Theory Ser. A 91 (1-2), pp. 464–475.
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Bailey’s Transform, Lemma, Chains and Tree.
In Special Functions 2000: Current Perspective and Future
Directions (Tempe, AZ), J. Bustoz, M. E. H. Ismail, and S. K. Suslov (Eds.),
NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 1–22.
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3: 17 q-Hypergeometric and Related Functions
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4: Bibliography B
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A Fortran-90 based multiprecision system.
ACM Trans. Math. Software 21 (4), pp. 379–387.
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Products of generalized hypergeometric series.
Proc. London Math. Soc. (2) 28 (2), pp. 242–254.
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Transformations of generalized hypergeometric series.
Proc. London Math. Soc. (2) 29 (2), pp. 495–502.
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The generating function of Jacobi polynomials.
J. London Math. Soc. 13, pp. 8–12.
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Generalized Hypergeometric Series.
Stechert-Hafner, Inc., New York.
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5: 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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An elliptic incarnation of the Bailey chain.
Int. Math. Res. Not. 2002 (37), pp. 1945–1977.
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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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6: 10.73 Physical Applications
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§10.73(i) Bessel and Modified Bessel Functions
►Bessel functions first appear in the investigation of a physical problem in Daniel Bernoulli’s analysis of the small oscillations of a uniform heavy flexible chain. … ►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). …7: 4.48 Software
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►See also Bailey (1995), Hull and Abrham (1986), Xu and Li (1994).
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Bailey (1993). Fortran.
8: 20 Theta Functions
Chapter 20 Theta Functions
…9: 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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A note on the trinomial analogue of Bailey’s lemma.
J. Combin. Theory Ser. A 81 (1), pp. 114–118.
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