Part of the book series: Grundlehren der mathematischen Wissenschaften (GL volume 141)AlgebraGeometrie und TensorkalkülTensorkalkül nebst AnwendungenInterpolation und genäherte QuadraturApproximation von FunktionenDarstellung von Funktionen in RechenautomatenLineare und nichtlineare Optimierung
I. Complex NumbersII. The Convergence of Infinite SeriesIII. Functions of a Complex VariableIV. Cauchy's TheoremV. Uniform ConvergenceVI. The Calculus of ResiduesVII. Integral FunctionsVIII. Conformal RepresentationIX. The Gamma FunctionX. The Hypergeometric FunctionsXI. Legendre FunctionsXII. Bessel FunctionsXIII. The Elliptic Functions of WeierstrassXIV. Jacobi's Elliptic FunctionsXV. Elliptic Modular Functions and Picard's Theorem
Translated by Frederick Bagemihl1. Introduction and Prerequisites2. Sequences and Series3. The Main Tests for Infinite Series. Operating with Convergent Series4. Power Series5. Development of the Theory of Convergence6. Expansion of the Elementary Functions7. Numerical and Closed Evaluation of Series
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