A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions, with an Account of the Principal Transcendental Functions |
Contents
CHAPTER PAGE I Complex Numbers | 3 |
The Theory of Convergence | 11 |
Continuous Functions and Uniform Convergence | 41 |
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a₁ absolutely convergent analytic function asymptotic expansion b₁ Bessel C₁ circle coefficients complex number constant continuous function contour convergent series converges absolutely converges uniformly Corollary cosh D₂ deduce defined denote differential equation doubly-periodic function e₁ ellipsoidal harmonics elliptic functions Example expression formula Fourier series given Hence hypergeometric independent infinite integer integral equation integrand Jacobi Journal für Math Lamé Lamé functions Laplace's equation London Math Mathieu functions Mathieu's obtained one-valued P₁ P₂ path of integration periodic points poles polynomial positive integer positive number Proc Prove real numbers result Riemann's satisfied series converges Shew shewn sin² singularities sn² solution tends to zero theorem theory Theta-functions values variable w₁ write