University of Illinois Urbana-Champaign

Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues

Reuter, Victoria

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Victoria_Reuter.pdf

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https://hdl.handle.net/2142/72779

Description

Title
Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues
Author(s)
Reuter, Victoria
Issue Date
2015-01-21
Director of Research (if dissertation) or Advisor (if thesis)
Berndt, Bruce C.
Doctoral Committee Chair(s)
Reznick, Bruce
Committee Member(s)
  • Berndt, Bruce C.
  • Hildebrand, A.J.
  • Stolarsky, Kenneth B.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2015-01-21T19:48:06Z
Keyword(s)
  • hypergeometric functions
  • continued fractions
  • gamma function
  • basic hypergeometric functions
  • q-analogue
  • q-series
  • Ramanujan
  • Ramanujan's notebooks
Abstract
Some of the most interesting of Ramanujan's continued fraction identities are those involving ratios of Gamma functions in Chapter 12 of his second notebook. This thesis develops a method for deriving such identities, using hypergeometric functions as the main tool. We begin by deriving a continued fraction identity, use it to prove Ramanujan's Entry 34, and then use the method to obtain new identities and relate them to two of Ramanujan's identities. We next prove Ramanujan's Entries 36 and 39. Finally, we rework the method for use with basic hypergeometric functions and use it to find q-analogues of the earlier new results.
Graduation Semester
2014-12
Permalink
http://hdl.handle.net/2142/72779
Copyright and License Information
Copyright 2014 Victoria Jane Reuter

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