This thesis deals with various aspects of development in the field of both ordinary and basic hypergeometric functions. It comprises six chapters. The first chapter gives a brief survey of some of the recents developments in this field including the work done in the present thesis. The second chapter gives a systematic study of the transformations connected with the partial sums of generalised hypergeometric series, both ordinary and basic. The main theorem proved in the chapter gives the most general relation of its type. The third chapter is concerned with the development of the transformation theory of bilateral cognate trigonometrical series and generalises all the known results in that field. The fourth chapter gives the integral analogues of some of the transformations of basic series analogous to those for the ordinary series in Chapter VI of Bailey's Cambridge Tract. The fifth chapter deals with a systematic classification and study of two and three term relations between special kinds of well-poised series of the type and gives a new method, by integrals, of deducing these transformations easily. The last and the sixth chapter gives a number of identities involving basic analogues of Appell's hypergeometric functions of two variables and some associated functions.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:703715 |
| Date | January 1953 |
| Creators | Agarwala, R. P. |
| Publisher | Royal Holloway, University of London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://repository.royalholloway.ac.uk/items/d5d12b9a-3cd2-4590-9dfe-e01d9c77287c/1/ |
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