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large a (or b) and c

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11: Bibliography F
  • S. Farid Khwaja and A. B. Olde Daalhuis (2014) Uniform asymptotic expansions for hypergeometric functions with large parameters IV. Anal. Appl. (Singap.) 12 (6), pp. 667–710.
  • J. L. Fields (1973) Uniform asymptotic expansions of certain classes of Meijer G -functions for a large parameter. SIAM J. Math. Anal. 4 (3), pp. 482–507.
  • J. L. Fields (1983) Uniform asymptotic expansions of a class of Meijer G -functions for a large parameter. SIAM J. Math. Anal. 14 (6), pp. 1204–1253.
  • 12: Preface
    Undoubtedly, the editors have overlooked some individuals who contributed, as is inevitable in a large long-lasting project. …
    13: 16.22 Asymptotic Expansions
    Asymptotic expansions of G p , q m , n ( z ; a ; b ) for large z are given in Luke (1969a, §§5.7 and 5.10) and Luke (1975, §5.9). …
    14: 12.11 Zeros
    When a > - 1 2 the zeros are asymptotically given by z a , s and z a , s ¯ , where s is a large positive integer and … For large negative values of a the real zeros of U ( a , x ) , U ( a , x ) , V ( a , x ) , and V ( a , x ) can be approximated by reversion of the Airy-type asymptotic expansions of §§12.10(vii) and 12.10(viii). …
    15: Bibliography W
  • T. Watanabe, M. Natori, and T. Oguni (Eds.) (1994) Mathematical Software for the P.C. and Work Stations – A Collection of Fortran 77 Programs. North-Holland Publishing Co., Amsterdam.
  • M. I. Weinstein and J. B. Keller (1985) Hill’s equation with a large potential. SIAM J. Appl. Math. 45 (2), pp. 200–214.
  • J. A. Wheeler (1937) Wave functions for large arguments by the amplitude-phase method. Phys. Rev. 52, pp. 1123–1127.
  • R. Wong (1973a) An asymptotic expansion of W k , m ( z ) with large variable and parameters. Math. Comp. 27 (122), pp. 429–436.
  • 16: Bibliography Z
  • S. Zhang and J. Jin (1996) Computation of Special Functions. John Wiley & Sons Inc., New York.
  • 17: 8.18 Asymptotic Expansions of I x ( a , b )
    Large a , Fixed b
    For asymptotic expansions for large values of a and/or b of the x -solution of the equation …
    18: Bibliography N
  • M. Nardin, W. F. Perger, and A. Bhalla (1992a) Algorithm 707: CONHYP: A numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes. ACM Trans. Math. Software 18 (3), pp. 345–349.
  • M. Nardin, W. F. Perger, and A. Bhalla (1992b) Numerical evaluation of the confluent hypergeometric function for complex arguments of large magnitudes. J. Comput. Appl. Math. 39 (2), pp. 193–200.
  • T. D. Newton (1952) Coulomb Functions for Large Values of the Parameter η . Technical report Atomic Energy of Canada Limited, Chalk River, Ontario.
  • Numerical Recipes (commercial C, C++, Fortran 77, and Fortran 90 libraries)
  • 19: 36.12 Uniform Approximation of Integrals
    where k is a large real parameter and y = { y 1 , y 2 , } is a set of additional (nonasymptotic) parameters. …
    20: 8.12 Uniform Asymptotic Expansions for Large Parameter
    Lastly, a uniform approximation for Γ ( a , a x ) for large a , with error bounds, can be found in Dunster (1996a). …