About the Project



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11: Bibliography H
  • E. Hille (1976) Ordinary Differential Equations in the Complex Domain. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York.
  • Y. P. Hsu (1993) Development of a Gaussian hypergeometric function code in complex domains. Internat. J. Modern Phys. C 4 (4), pp. 805–840.
  • L. K. Hua (1963) Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains. Translations of Mathematical Monographs, Vol. 6, American Mathematical Society, Providence, RI.
  • 12: 3.7 Ordinary Differential Equations
    where f , g , and h are analytic functions in a domain D . … Assume that we wish to integrate (3.7.1) along a finite path 𝒫 from z = a to z = b in a domain D . The path is partitioned at P + 1 points labeled successively z 0 , z 1 , , z P , with z 0 = a , z P = b . …
    13: 2.5 Mellin Transform Methods
    The domain of analyticity of f ( z ) is usually an infinite strip a < z < b parallel to the imaginary axis. …
    Table 2.5.1: Domains of convergence for Mellin transforms.
    Transform Domain of Convergence
    Next from Table 2.5.1 we observe that the integrals for the transform pair f j ( 1 - z ) and h k ( z ) are absolutely convergent in the domain D j k specified in Table 2.5.2, and these domains are nonempty as a consequence of (2.5.19) and (2.5.20).
    Table 2.5.2: Domains of analyticity for Mellin transforms.
    Transform Pair Domain D j k
    From Table 2.5.2, we see that each G j k ( z ) is analytic in the domain D j k . …
    14: 10.20 Uniform Asymptotic Expansions for Large Order
    The eye-shaped closed domain in the uncut z -plane that is bounded by B P 1 E 1 and B P 2 E 2 is denoted by K ; see Figure 10.20.3. …
    See accompanying text
    Figure 10.20.3: z -plane. Domain K (unshaded). … Magnify
    15: Preface
    The associate editors are eminent domain experts who were recruited to advise the project on strategy, execution, subject content, format, and presentation, and to help identify and recruit suitable candidate authors and validators. …
    16: 13.9 Zeros
    Let P α denote the closure of the domain that is bounded by the parabola y 2 = 4 α ( x + α ) and contains the origin. …
    17: Bibliography J
  • W. B. Jones and W. J. Thron (1985) On the computation of incomplete gamma functions in the complex domain. J. Comput. Appl. Math. 12/13, pp. 401–417.
  • 18: Bibliography N
  • V. Yu. Novokshënov (1990) The Boutroux ansatz for the second Painlevé equation in the complex domain. Izv. Akad. Nauk SSSR Ser. Mat. 54 (6), pp. 1229–1251 (Russian).
  • 19: Bibliography R
  • D. St. P. Richards (Ed.) (1992) Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications. Contemporary Mathematics, Vol. 138, American Mathematical Society, Providence, RI.
  • 20: Bibliography K
  • A. A. Kapaev and A. V. Kitaev (1993) Connection formulae for the first Painlevé transcendent in the complex domain. Lett. Math. Phys. 27 (4), pp. 243–252.
  • M. K. Kerimov and S. L. Skorokhodov (1984a) Calculation of modified Bessel functions in a complex domain. Zh. Vychisl. Mat. i Mat. Fiz. 24 (5), pp. 650–664.
  • T. H. Koornwinder (1992) Askey-Wilson Polynomials for Root Systems of Type B C . In Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications (Tampa, FL, 1991), Contemp. Math., Vol. 138, pp. 189–204.