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11: Bibliography P
  • R. B. Paris (1991) The asymptotic behaviour of Pearcey’s integral for complex variables. Proc. Roy. Soc. London Ser. A 432 (1886), pp. 391–426.
  • R. B. Paris (1992a) Smoothing of the Stokes phenomenon for high-order differential equations. Proc. Roy. Soc. London Ser. A 436, pp. 165–186.
  • R. B. Paris (2001a) On the use of Hadamard expansions in hyperasymptotic evaluation. I. Real variables. Proc. Roy. Soc. London Ser. A 457 (2016), pp. 2835–2853.
  • R. B. Paris (2001b) On the use of Hadamard expansions in hyperasymptotic evaluation. II. Complex variables. Proc. Roy. Soc. London Ser. A 457, pp. 2855–2869.
  • R. B. Paris (2002c) Exponential asymptotics of the Mittag-Leffler function. Proc. Roy. Soc. London Ser. A 458, pp. 3041–3052.
  • 12: Bibliography J
  • H. Jeffreys (1928) The effect on Love waves of heterogeneity in the lower layer. Monthly Notices Roy. Astronom. Soc. Geophysical Supplement 2, pp. 101–111.
  • A. Jonquière (1889) Note sur la série n = 1 x n / n s . Bull. Soc. Math. France 17, pp. 142–152 (French).
  • G. S. Joyce (1973) On the simple cubic lattice Green function. Philos. Trans. Roy. Soc. London Ser. A 273, pp. 583–610.
  • G. S. Joyce (1994) On the cubic lattice Green functions. Proc. Roy. Soc. London Ser. A 445, pp. 463–477.
  • B. R. Judd (1976) Modifications of Coulombic interactions by polarizable atoms. Math. Proc. Cambridge Philos. Soc. 80 (3), pp. 535–539.
  • 13: Bibliography N
  • A. Nakamura (1996) Toda equation and its solutions in special functions. J. Phys. Soc. Japan 65 (6), pp. 1589–1597.
  • G. Nemes (2014a) Error bounds and exponential improvement for the asymptotic expansion of the Barnes G -function. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 470 (2172), pp. 20140534, 14.
  • P. G. Nevai (1979) Orthogonal polynomials. Mem. Amer. Math. Soc. 18 (213), pp. v+185 pp..
  • J. F. Nye (2006) Dislocation lines in the hyperbolic umbilic diffraction catastrophe. Proc. Roy. Soc. Lond. Ser. A 462, pp. 2299–2313.
  • J. F. Nye (2007) Dislocation lines in the swallowtail diffraction catastrophe. Proc. Roy. Soc. Lond. Ser. A 463, pp. 343–355.
  • 14: Bibliography S
  • M. J. Seaton and G. Peach (1962) The determination of phases of wave functions. Proc. Phys. Soc. 79 (6), pp. 1296–1297.
  • B. D. Sleeman (1969) Non-linear integral equations for Heun functions. Proc. Edinburgh Math. Soc. (2) 16, pp. 281–289.
  • A. Sri Ranga (2010) Szegő polynomials from hypergeometric functions. Proc. Amer. Math. Soc. 138 (12), pp. 4259–4270.
  • J. Steinig (1972) The sign of Lommel’s function. Trans. Amer. Math. Soc. 163, pp. 123–129.
  • O. Szász (1951) On the relative extrema of the Hermite orthogonal functions. J. Indian Math. Soc. (N.S.) 15, pp. 129–134.
  • 15: Bibliography G
  • G. Gasper (1972) An inequality of Turán type for Jacobi polynomials. Proc. Amer. Math. Soc. 32, pp. 435–439.
  • J. A. Gaunt (1929) The triplets of helium. Philos. Trans. Roy. Soc. London Ser. A 228, pp. 151–196.
  • S. Goldstein (1927) Mathieu functions. Trans. Camb. Philos. Soc. 23, pp. 303–336.
  • H. Gupta (1935) A table of partitions. Proc. London Math. Soc. (2) 39, pp. 142–149.
  • H. Gupta (1937) A table of partitions (II). Proc. London Math. Soc. (2) 42, pp. 546–549.
  • 16: Bibliography E
  • D. Elliott (1998) The Euler-Maclaurin formula revisited. J. Austral. Math. Soc. Ser. B 40 (E), pp. E27–E76 (electronic).
  • A. Erdélyi (1941a) Generating functions of certain continuous orthogonal systems. Proc. Roy. Soc. Edinburgh. Sect. A. 61, pp. 61–70.
  • T. Estermann (1959) On the representations of a number as a sum of three squares. Proc. London Math. Soc. (3) 9, pp. 575–594.
  • W. N. Everitt and D. S. Jones (1977) On an integral inequality. Proc. Roy. Soc. London Ser. A 357, pp. 271–288.
  • 17: Bibliography Y
  • T. Yoshida (1995) Computation of Kummer functions U ( a , b , x ) for large argument x by using the τ -method. Trans. Inform. Process. Soc. Japan 36 (10), pp. 2335–2342 (Japanese).
  • 18: Bibliography R
  • H. Rademacher (1938) On the partition function p(n). Proc. London Math. Soc. (2) 43 (4), pp. 241–254.
  • S. Ramanujan (1927) Some properties of Bernoulli’s numbers (J. Indian Math. Soc. 3 (1911), 219–234.). In Collected Papers,
  • D. L. Rod and B. D. Sleeman (1995) Complexity in spatio-temporal dynamics. Proc. Roy. Soc. Edinburgh Sect. A 125 (5), pp. 959–974.
  • R. R. Rosales (1978) The similarity solution for the Korteweg-de Vries equation and the related Painlevé transcendent. Proc. Roy. Soc. London Ser. A 361, pp. 265–275.
  • 19: Bibliography L
  • L. J. Landau (2000) Bessel functions: Monotonicity and bounds. J. London Math. Soc. (2) 61 (1), pp. 197–215.
  • R. E. Langer (1934) The solutions of the Mathieu equation with a complex variable and at least one parameter large. Trans. Amer. Math. Soc. 36 (3), pp. 637–695.
  • W. Lay and S. Yu. Slavyanov (1999) Heun’s equation with nearby singularities. Proc. Roy. Soc. London Ser. A 455, pp. 4347–4361.
  • E. R. Love (1972a) Addendum to: “Changing the order of integration”. J. Austral. Math. Soc. 14, pp. 383–384.
  • E. R. Love (1972b) Two index laws for fractional integrals and derivatives. J. Austral. Math. Soc. 14, pp. 385–410.
  • 20: Bibliography F
  • S. Fempl (1960) Sur certaines sommes des intégral-cosinus. Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
  • J. L. Fields (1966) A note on the asymptotic expansion of a ratio of gamma functions. Proc. Edinburgh Math. Soc. (2) 15, pp. 43–45.
  • C. K. Frederickson and P. L. Marston (1992) Transverse cusp diffraction catastrophes produced by the reflection of ultrasonic tone bursts from a curved surface in water. J. Acoust. Soc. Amer. 92 (5), pp. 2869–2877.
  • C. K. Frederickson and P. L. Marston (1994) Travel time surface of a transverse cusp caustic produced by reflection of acoustical transients from a curved metal surface. J. Acoust. Soc. Amer. 95 (2), pp. 650–660.
  • Y. V. Fyodorov (2005) Introduction to the Random Matrix Theory: Gaussian Unitary Ensemble and Beyond. In Recent Perspectives in Random Matrix Theory and Number Theory, London Math. Soc. Lecture Note Ser., Vol. 322, pp. 31–78.