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About Generalized Hypergeometric Series
<p>Before the year 1923 the literature dealing with generalized</p><p>hypergeometric series was somewhat scattered, but in that year</p><p>Professor G. H. Hardy published his paper ''A chapter from Ra-</p><p>manujan's note-book" in which he gave an account and proofs of</p><p>the results then known, most of which had been rediscovered by</p><p>Ramanujan. Since then numerous papers have been written on</p><p>the subject, and it seems desirable that the mass of special results,</p><p>obtained by one method or another, should be collected together.</p><p>This is the primary object of this tract.</p><p>No attempt has been made to give a complete account of the</p><p>ordinary hypergeometric series. In fact the first chapter simply</p><p>gives the minimum required for the succeeding chapters. Again,</p><p>all parts of the subject, such as asymptotic expansions, which</p><p>definitely belong to function theory, have been deliberately</p><p>ignored.</p><p>Although the main part of the work deals with generalized</p><p>hypergeometric series, there are also short accounts of Heine's</p><p>basic hypergeometric series and Appell's hypergeometric func-</p><p>tions of two variables .</p><p>.My thanks are due to Professor G. H. Hardy who made valuable</p><p>suggestions regarding the general plan of the work, and to</p><p>Professor L. J. Mordell who suggested the desirability of a tract</p><p>on this subject.</p>
Detailed Information
| Author: | G. H. HARDY, |
|---|---|
| Publication Year: | 1935 |
| Pages: | 108 |
| Language: | other |
| File Size: | 3.3648 |
| Format: | |
| Price: | FREE |
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