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1: Bibliography Y
  • A. Yu. Yeremin, I. E. Kaporin, and M. K. Kerimov (1985) The calculation of the Riemann zeta function in the complex domain. USSR Comput. Math. and Math. Phys. 25 (2), pp. 111–119.
  • A. Yu. Yeremin, I. E. Kaporin, and M. K. Kerimov (1988) Computation of the derivatives of the Riemann zeta-function in the complex domain. USSR Comput. Math. and Math. Phys. 28 (4), pp. 115–124.
  • 2: 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 . …
    3: 1.10 Functions of a Complex Variable
    Let f 1 ( z ) be analytic in a domain D 1 . … Suppose the subarc z ( t ) , t [ t j 1 , t j ] is contained in a domain D j , j = 1 , , n . … If f ( z ) is analytic in a domain D , z 0 D and | f ( z ) | | f ( z 0 ) | for all z D , then f ( z ) is a constant in D . … Assume that for each t [ a , b ] , f ( z , t ) is an analytic function of z in D , and also that f ( z , t ) is a continuous function of both variables. … Suppose a n = a n ( z ) , z D , a domain. …
    4: 1.9 Calculus of a Complex Variable
    A domain D , say, is an open set in that is connected, that is, any two points can be joined by a polygonal arc (a finite chain of straight-line segments) lying in the set. … A function f ( z ) is analytic in a domain D if it is analytic at each point of D . … … Suppose f ( z ) is analytic in a domain D and C 1 , C 2 are two arcs in D passing through z 0 . … Suppose the series n = 0 f n ( z ) , where f n ( z ) is continuous, converges uniformly on every compact set of a domain D , that is, every closed and bounded set in D . …
    5: 1.13 Differential Equations
    A domain in the complex plane is simply-connected if it has no “holes”; more precisely, if its complement in the extended plane { } is connected. … where z D , a simply-connected domain, and f ( z ) , g ( z ) are analytic in D , has an infinite number of analytic solutions in D . …
    1.13.6 A w 1 ( z ) + B w 2 ( z ) = 0 , z D ,
    6: Bibliography W
  • R. Wong and Y. Zhao (2004) Uniform asymptotic expansion of the Jacobi polynomials in a complex domain. Proc. Roy. Soc. London Ser. A 460, pp. 2569–2586.
  • 7: 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.
  • 8: 3.10 Continued Fractions
    However, other continued fractions with the same limit may converge in a much larger domain of the complex plane than the fraction given by (3.10.4) and (3.10.5). …
    9: 3.3 Interpolation
    If f is analytic in a simply-connected domain D 1.13(i)), then for z D , … If f is analytic in a simply-connected domain D , then for z D , …
    10: Bibliography H
  • Y. P. Hsu (1993) Development of a Gaussian hypergeometric function code in complex domains. Internat. J. Modern Phys. C 4 (4), pp. 805–840.