Cauchy–Riemann equations
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1: 1.9 Calculus of a Complex Variable
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Cauchy–Riemann Equations
…2: Bibliography H
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Tables of the Riemann Zeta Function.
Royal Society Mathematical Tables, Vol. 6, Cambridge University Press, New York.
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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.
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Definitions of Stieltjes Integrals of the Riemann Type.
Amer. Math. Monthly 45 (5), pp. 265–278.
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Poncelet Polygons and the Painlevé Equations.
In Geometry and Analysis (Bombay, 1992), Ramanan (Ed.),
pp. 151–185.
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Estimates of the stability intervals for Hill’s equation.
Proc. Amer. Math. Soc. 14 (6), pp. 930–932.
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3: 1.4 Calculus of One Variable
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Riemann Integrals
… ►If the limit exists then is called Riemann integrable. … ►A generalization of the Riemann integral is the Stieltjes integral , where is a nondecreasing function on the closure of , which may be bounded, or unbounded, and is the Stieltjes measure. …Stieltjes integrability for with respect to can be defined similarly as Riemann integrability in the case that is differentiable with respect to ; a generalization follows below. … ►Cauchy Principal Values
…4: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►An inner product space is called a Hilbert space if every Cauchy sequence in (i.
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►Equation (1.18.19) is often called the completeness relation.
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►Applying equations (1.18.29) and (1.18.30), the complete set of normalized eigenfunctions being
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► See §18.39 for discussion of Schrödinger equations and operators.
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