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Cauchy–Riemann equations

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1: 1.9 Calculus of a Complex Variable
CauchyRiemann Equations
2: Bibliography H
  • C. B. Haselgrove and J. C. P. Miller (1960) Tables of the Riemann Zeta Function. Royal Society Mathematical Tables, Vol. 6, Cambridge University Press, New York.
  • P. Henrici (1986) Applied and Computational Complex Analysis. Vol. 3: Discrete Fourier Analysis—Cauchy Integrals—Construction of Conformal Maps—Univalent Functions. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons Inc.], New York.
  • T. H. Hildebrandt (1938) Definitions of Stieltjes Integrals of the Riemann Type. Amer. Math. Monthly 45 (5), pp. 265–278.
  • N. J. Hitchin (1995) Poncelet Polygons and the Painlevé Equations. In Geometry and Analysis (Bombay, 1992), Ramanan (Ed.), pp. 151–185.
  • H. Hochstadt (1963) Estimates of the stability intervals for Hill’s equation. Proc. Amer. Math. Soc. 14 (6), pp. 930–932.
  • 3: 1.4 Calculus of One Variable
    Riemann Integrals
    If the limit exists then f is called Riemann integrable. … A generalization of the Riemann integral is the Stieltjes integral a b f ( x ) d α ( x ) , where α ( x ) is a nondecreasing function on the closure of ( a , b ) , which may be bounded, or unbounded, and d α ( x ) is the Stieltjes measure. …Stieltjes integrability for f with respect to α can be defined similarly as Riemann integrability in the case that α ( x ) is differentiable with respect to x ; a generalization follows below. …
    Cauchy Principal Values
    4: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
    An inner product space V is called a Hilbert space if every Cauchy sequence { v n } in V (i. … Equation (1.18.19) is often called the completeness relation. … Applying equations (1.18.29) and (1.18.30), the complete set of normalized eigenfunctions being … See §18.39 for discussion of Schrödinger equations and operators. …