Mathematical Sciences: Orthogonal Polynomials and Some of   Their Applications
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{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
Several specific topics will be addressed in this project.              The first of these concerns Wilson polynomials - these are a                    general class of polynomials governed by four parameters and are                related to classical hypergeometric functions (appearing as seems               of the initial segments of these functions).  Work will be done                 on asymptotic expansions of polynomials as certain of the                       parameters increase withound bound.  The work is motivated by                   problems in combinatorial design.                                                       A second area of research concerns continued fraction                   expansions of quotients of hypergeometric functions.   This idea                can be traced back to work of Gauss and continues to be of                      interest because convergent positive continued fractions are                    Stieltjes transforms of the positive measure against which the                  denominator polynomials are otrhogonal.  Ultimately one will want               to invert the transform to find the elusive measure.                                    Another direction represents a continuation of the principal            investigator's work on Askey-Wilson integrals.  Some remarkable                 applications of special functions have been made to the                         evaluation of complex definite integrals.  The Askey-Wilson                     example was one in which an unexpected combinatorial evaluation                 was discovered.  The current work, in collaboration with Dennis                 Stanton, will seek to flesh out the fundamental ideas behind this               discovery.  They will begin with a particularly simple class of                 polynomials and seek to connect the integral of products of these               polynomials with basic identities found in decompositions of                    multipartite graphs.
{'FirstName': 'Mourad', 'LastName': 'Ismail', 'PI_MID_INIT': 'E', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Mourad E Ismail', 'EmailAddress': 'ismail@math.ucf.edu', 'NSF_ID': '000333118', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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