2014 Reprint of 1962 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions, categories that are similar in some ways, but different in others. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not hold generally for real analytic functions. The richness of material provided in Vekua's book should make it an excellent reference book, but a reader who is interested only in getting a brief and concise idea about the basic facts of GAF may find himself lost in the bulk of material especially since 129 pages of hard analysis precede the introduction of the GAF. The book presupposes some knowledge of Lebesgue integration and the elements of functional analysis.

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