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algebraic analytic function apply arbitrary operators assume axis Banach space calculation Chapter characteristic equation class 9C class Q complex numbers Consequently constant continuous derivative continuous function convolution corresponding defined definition denote determine differential equation divisor electromotive force equal to zero Example exist exponential function expression factors finite interval formula four-terminal network function x(X functions of class given graph impedance implies initial conditions instance irreducible irreducible polynomials Laplace transform linear linearly independent solutions locally integrable functions logarithmic matrix method multiplying number of linearly obtain operational calculus operational equation operational function ordinary parametric function partial equation positive number power series proof properties prove radius of convergence represented right side roots satisfies equation satisfy the equation satisfying conditions sequence short-circuit current solution of equation solve string Substituting Suppose term theorem tion translation operator uniform convergence uniformly unique values vanishes variable voltage whence write