Jacobi%20identity
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1: 20.7 Identities
§20.7 Identities
… ►Also, in further development along the lines of the notations of Neville (§20.1) and of Glaisher (§22.2), the identities (20.7.6)–(20.7.9) have been recast in a more symmetric manner with respect to suffices . … ►§20.7(v) Watson’s Identities
… ►See Lawden (1989, pp. 19–20). This reference also gives the eleven additional identities for the permutations of the four theta functions. …2: 20.11 Generalizations and Analogs
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►This is the discrete analog of the Poisson identity (§1.8(iv)).
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►This is Jacobi’s inversion problem of §20.9(ii).
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►Each provides an extension of Jacobi’s inversion problem.
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3: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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Rogers-Ramanujan identities in the hard hexagon model.
J. Statist. Phys. 26 (3), pp. 427–452.
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Rogers-Ramanujan Identities: A Century of Progress from Mathematics to Physics.
In Proceedings of the International Congress of Mathematicians,
Vol. III (Berlin, 1998),
pp. 163–172.
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Phase-space projection identities for diffraction catastrophes.
J. Phys. A 13 (1), pp. 149–160.
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A cubic counterpart of Jacobi’s identity and the AGM.
Trans. Amer. Math. Soc. 323 (2), pp. 691–701.
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4: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Cyclic identities for Jacobi elliptic and related functions.
J. Math. Phys. 44 (4), pp. 1822–1841.
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Cyclic identities involving Jacobi elliptic functions.
J. Math. Phys. 43 (7), pp. 3798–3806.
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Dilogarithm identities.
Progr. Theoret. Phys. Suppl. (118), pp. 61–142.
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5: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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An elementary proof of the Macdonald identities for
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Adv. in Math. 57 (1), pp. 34–70.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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6: Bibliography D
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Novel identities for simple - symbols.
J. Mathematical Phys. 16, pp. 318–319.
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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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Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions.
Methods Appl. Anal. 6 (3), pp. 21–56.
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Product formulas and Nicholson-type integrals for Jacobi functions. I. Summary of results.
SIAM J. Math. Anal. 9 (1), pp. 76–86.
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7: Bibliography L
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Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
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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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Lie algebraic approaches to classical partition identities.
Adv. in Math. 29 (1), pp. 15–59.
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A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities.
Adv. in Math. 45 (1), pp. 21–72.
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Co-recursive associated Jacobi polynomials.
J. Comput. Appl. Math. 57 (1-2), pp. 203–213.
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