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1: Bibliography Q
  • W.-Y. Qiu and R. Wong (2000) Uniform asymptotic expansions of a double integral: Coalescence of two stationary points. Proc. Roy. Soc. London Ser. A 456, pp. 407–431.
  • C. K. Qu and R. Wong (1999) “Best possible” upper and lower bounds for the zeros of the Bessel function J ν ( x ) . Trans. Amer. Math. Soc. 351 (7), pp. 2833–2859.
  • 2: Bibliography U
  • F. Ursell (1972) Integrals with a large parameter. Several nearly coincident saddle-points. Proc. Cambridge Philos. Soc. 72, pp. 49–65.
  • F. Ursell (1980) Integrals with a large parameter: A double complex integral with four nearly coincident saddle-points. Math. Proc. Cambridge Philos. Soc. 87 (2), pp. 249–273.
  • F. Ursell (1984) Integrals with a large parameter: Legendre functions of large degree and fixed order. Math. Proc. Cambridge Philos. Soc. 95 (2), pp. 367–380.
  • K. M. Urwin and F. M. Arscott (1970) Theory of the Whittaker-Hill equation. Proc. Roy. Soc. Edinburgh Sect. A 69, pp. 28–44.
  • 3: Bibliography O
  • A. B. Olde Daalhuis (1998a) Hyperasymptotic solutions of higher order linear differential equations with a singularity of rank one. Proc. Roy. Soc. London Ser. A 454, pp. 1–29.
  • A. B. Olde Daalhuis (2004a) Inverse factorial-series solutions of difference equations. Proc. Edinb. Math. Soc. (2) 47 (2), pp. 421–448.
  • A. B. Olde Daalhuis (2005a) Hyperasymptotics for nonlinear ODEs. I. A Riccati equation. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2060), pp. 2503–2520.
  • A. B. Olde Daalhuis (2005b) Hyperasymptotics for nonlinear ODEs. II. The first Painlevé equation and a second-order Riccati equation. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2062), pp. 3005–3021.
  • F. W. J. Olver (1977c) Second-order differential equations with fractional transition points. Trans. Amer. Math. Soc. 226, pp. 227–241.
  • 4: Bibliography W
  • G. N. Watson (1937) Two tables of partitions. Proc. London Math. Soc. (2) 42, pp. 550–556.
  • F. J. W. Whipple (1927) Some transformations of generalized hypergeometric series. Proc. London Math. Soc. (2) 26 (2), pp. 257–272.
  • J. Wimp (1964) A class of integral transforms. Proc. Edinburgh Math. Soc. (2) 14, pp. 33–40.
  • J. Wimp (1965) On the zeros of a confluent hypergeometric function. Proc. Amer. Math. Soc. 16 (2), pp. 281–283.
  • E. M. Wright (1935) The asymptotic expansion of the generalized Bessel function. Proc. London Math. Soc. (2) 38, pp. 257–270.
  • 5: Bibliography B
  • W. N. Bailey (1928) Products of generalized hypergeometric series. Proc. London Math. Soc. (2) 28 (2), pp. 242–254.
  • W. N. Bailey (1929) Transformations of generalized hypergeometric series. Proc. London Math. Soc. (2) 29 (2), pp. 495–502.
  • W. N. Bailey (1938) The generating function of Jacobi polynomials. J. London Math. Soc. 13, pp. 8–12.
  • H. Bateman (1905) A generalisation of the Legendre polynomial. Proc. London Math. Soc. (2) 3 (3), pp. 111–123.
  • M. V. Berry (1966) Uniform approximation for potential scattering involving a rainbow. Proc. Phys. Soc. 89 (3), pp. 479–490.
  • 6: Bibliography I
  • E. L. Ince (1932) Tables of the elliptic cylinder functions. Proc. Roy. Soc. Edinburgh Sect. A 52, pp. 355–433.
  • E. L. Ince (1940a) The periodic Lamé functions. Proc. Roy. Soc. Edinburgh 60, pp. 47–63.
  • E. L. Ince (1940b) Further investigations into the periodic Lamé functions. Proc. Roy. Soc. Edinburgh 60, pp. 83–99.
  • M. E. H. Ismail and D. R. Masson (1994) q -Hermite polynomials, biorthogonal rational functions, and q -beta integrals. Trans. Amer. Math. Soc. 346 (1), pp. 63–116.
  • M. E. H. Ismail and X. Li (1992) Bound on the extreme zeros of orthogonal polynomials. Proc. Amer. Math. Soc. 115 (1), pp. 131–140.
  • 7: Bibliography
  • C. Adiga, B. C. Berndt, S. Bhargava, and G. N. Watson (1985) Chapter 16 of Ramanujan’s second notebook: Theta-functions and q -series. Mem. Amer. Math. Soc. 53 (315), pp. v+85.
  • G. B. Airy (1838) On the intensity of light in the neighbourhood of a caustic. Trans. Camb. Phil. Soc. 6, pp. 379–402.
  • M. Alam (1979) Zeros of Stieltjes and Van Vleck polynomials. Trans. Amer. Math. Soc. 252, pp. 197–204.
  • G. E. Andrews (1972) Summations and transformations for basic Appell series. J. London Math. Soc. (2) 4, pp. 618–622.
  • F. M. Arscott (1959) A new treatment of the ellipsoidal wave equation. Proc. London Math. Soc. (3) 9, pp. 21–50.
  • 8: Bibliography D
  • P. Dean (1966) The constrained quantum mechanical harmonic oscillator. Proc. Cambridge Philos. Soc. 62, pp. 277–286.
  • A. Decarreau, M.-Cl. Dumont-Lepage, P. Maroni, A. Robert, and A. Ronveaux (1978a) Formes canoniques des équations confluentes de l’équation de Heun. Ann. Soc. Sci. Bruxelles Sér. I 92 (1-2), pp. 53–78.
  • A. Decarreau, P. Maroni, and A. Robert (1978b) Sur les équations confluentes de l’équation de Heun. Ann. Soc. Sci. Bruxelles Sér. I 92 (3), pp. 151–189.
  • D. Ding (2000) A simplified algorithm for the second-order sound fields. J. Acoust. Soc. Amer. 108 (6), pp. 2759–2764.
  • J. Dougall (1907) On Vandermonde’s theorem, and some more general expansions. Proc. Edinburgh Math. Soc. 25, pp. 114–132.
  • 9: Bibliography H
  • A. J. S. Hamilton (2001) Formulae for growth factors in expanding universes containing matter and a cosmological constant. Monthly Notices Roy. Astronom. Soc. 322 (2), pp. 419–425.
  • E. Hille (1929) Note on some hypergeometric series of higher order. J. London Math. Soc. 4, pp. 50–54.
  • N. J. Hitchin (2003) A lecture on the octahedron. Bull. London Math. Soc. 35 (5), pp. 577–600.
  • H. Hochstadt (1963) Estimates of the stability intervals for Hill’s equation. Proc. Amer. Math. Soc. 14 (6), pp. 930–932.
  • C. J. Howls (1992) Hyperasymptotics for integrals with finite endpoints. Proc. Roy. Soc. London Ser. A 439, pp. 373–396.
  • 10: Bibliography C
  • L. Carlitz (1954a) q -Bernoulli and Eulerian numbers. Trans. Amer. Math. Soc. 76 (2), pp. 332–350.
  • B. C. Carlson (1970) Inequalities for a symmetric elliptic integral. Proc. Amer. Math. Soc. 25 (3), pp. 698–703.
  • C. J. Chapman (1999) Caustics in cylindrical ducts. Proc. Roy. Soc. London Ser. A 455, pp. 2529–2548.
  • T. M. Cherry (1948) Expansions in terms of parabolic cylinder functions. Proc. Edinburgh Math. Soc. (2) 8, pp. 50–65.
  • B. K. Choudhury (1995) The Riemann zeta-function and its derivatives. Proc. Roy. Soc. London Ser. A 450, pp. 477–499.