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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 2 , 3 , 4 . …
§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
This is the discrete analog of the Poisson identity1.8(iv)). … This is Jacobi’s inversion problem of §20.9(ii). … Each provides an extension of Jacobi’s inversion problem. …
3: Bibliography B
  • G. Backenstoss (1970) Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.
  • R. J. Baxter (1981) Rogers-Ramanujan identities in the hard hexagon model. J. Statist. Phys. 26 (3), pp. 427–452.
  • A. Berkovich and B. M. McCoy (1998) 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.
  • M. V. Berry and F. J. Wright (1980) Phase-space projection identities for diffraction catastrophes. J. Phys. A 13 (1), pp. 149–160.
  • J. M. Borwein and P. B. Borwein (1991) A cubic counterpart of Jacobi’s identity and the AGM. Trans. Amer. Math. Soc. 323 (2), pp. 691–701.
  • 4: Bibliography K
  • R. B. Kearfott, M. Dawande, K. Du, and C. Hu (1994) Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.
  • M. K. Kerimov (1980) Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
  • A. Khare, A. Lakshminarayan, and U. Sukhatme (2003) Cyclic identities for Jacobi elliptic and related functions. J. Math. Phys. 44 (4), pp. 1822–1841.
  • A. Khare and U. Sukhatme (2002) Cyclic identities involving Jacobi elliptic functions. J. Math. Phys. 43 (7), pp. 3798–3806.
  • A. N. Kirillov (1995) Dilogarithm identities. Progr. Theoret. Phys. Suppl. (118), pp. 61–142.
  • 5: Bibliography M
  • A. J. MacLeod (1996b) Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.
  • Fr. Mechel (1966) Calculation of the modified Bessel functions of the second kind with complex argument. Math. Comp. 20 (95), pp. 407–412.
  • R. Metzler, J. Klafter, and J. Jortner (1999) 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.
  • S. C. Milne (1985b) An elementary proof of the Macdonald identities for A l ( 1 ) . Adv. in Math. 57 (1), pp. 34–70.
  • D. S. Moak (1981) The q -analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81 (1), pp. 20–47.
  • 6: Bibliography D
  • B. Döring (1966) Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.
  • B. I. Dunlap and B. R. Judd (1975) Novel identities for simple n - j symbols. J. Mathematical Phys. 16, pp. 318–319.
  • T. M. Dunster (1989) Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.
  • T. M. Dunster (1999) Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions. Methods Appl. Anal. 6 (3), pp. 21–56.
  • L. Durand (1978) Product formulas and Nicholson-type integrals for Jacobi functions. I. Summary of results. SIAM J. Math. Anal. 9 (1), pp. 76–86.
  • 7: Bibliography L
  • P. W. Lawrence, R. M. Corless, and D. J. Jeffrey (2012) Algorithm 917: complex double-precision evaluation of the Wright ω function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
  • D. J. Leeming (1977) An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.
  • J. Lepowsky and S. Milne (1978) Lie algebraic approaches to classical partition identities. Adv. in Math. 29 (1), pp. 15–59.
  • J. Lepowsky and R. L. Wilson (1982) A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities. Adv. in Math. 45 (1), pp. 21–72.
  • J. Letessier (1995) Co-recursive associated Jacobi polynomials. J. Comput. Appl. Math. 57 (1-2), pp. 203–213.