Analysis I pp 1-81

# Series and Integral Representations

• M. A. Evgrafov
Chapter
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 13)

## Abstract

Infinite series, and their analogues—integral representations, became fundamental tools in mathematical analysis, starting in the second half of the seventeenth century. They have provided the means for introducing into analysis all of the so-called transcendental functions, including those which are now called elementary (the logarithm, exponential and trigonometric functions). With their help the solutions of many differential equations, both ordinary and partial, have been found. In fact the whole development of mathematical analysis from Newton up to the end of the nineteenth century was in the closest way connected with the development of the apparatus of series and integral representations. Moreover, many abstract divisions of mathematics (for example, functional analysis) arose and were developed in order to study series.

## Keywords

Singular Point Power Series Integral Representation Analytic Continuation Formal Series
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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