Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.529774
Title: Functions of hypergeometric type
Author: Slater, L. J.
Awarding Body: University of London
Current Institution: Royal Holloway, University of London
Date of Award: 1951
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Abstract:
This thesis deals with a method of expressing, as infinite products, some special limiting cases of a general transformation (2,4) between basic hypergeometric series. A short historical introduction (1.2), is followed by some preliminary theorems on the transformation of infinite series (2.1)--(2.3), a proof of the basic transformation, and a discussion of the work of L.J. Rogers (3.1)--(3.2). Rogers expressed a number of these limiting cases of hypergeometric functions in terms of infinite products by using trigonometrical identities, and, in particular, a sketch is given of his method of deducing the group of series called by him, A-series. A new method is then given (4.1)--(4.6) of deducing these A-series, using basic bilateral series. By employing W.N. Bailey's summation theorem for the bilateral series, all the transformations given by Rogers, are deduced, together with a number of new transformations, (4.7). Limiting cases of these special transformations are then considered (5.1.)--(5.3) and lead to the deduction of a large number of special identities of the Rogers-Hamanujan type, (5.4)--(6.3). Of these about forty involving products of the types [equations] are believed to be new. Two proofs are then given of the summation theorem (7.1)--(7.2), and a generalisation (7.4) of the original basic transformation, some equivalent product theorems (5.3), (7.3) and (7.5) are also considered, end the thesis concludes with an appendix containing a list of one hundred and thirty identities, which have been deduced in the body of the thesis.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.529774  DOI: Not available
Keywords: Mathematics
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