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CHAPTER tkat I Complex Numbers
The Theory of Convergence
Continuous Functions and Uniform Convergence
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absolutely convergent addition-theorem analytic function asymptotic expansion Bessel bounded circle coefficients complex number condition consider constant continuous function contour convergent series converges absolutely converges uniformly Corollary corresponding cosh curve deduce defined definition denote determine differential equation doubly-periodic function ellipsoidal harmonics elliptic functions Example exists expression follows formula Fourier series given Hence hypergeometric independent infinite infinity integer integral equation integrand interval Jacobi Jacobian elliptic functions Journal fur Math Laplace's equation Legendre functions limit linear London Math Mathieu functions modulus multiplied notation obtained one-valued path of integration periodic points polynomial positive integer positive number Proc proof Prove radius range reader real axis real numbers real values residues result Riemann's roots series converges Shew shewn singularities tends to zero theorem theory Theta-functions Trip uniformly convergent vanish write