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THE SHEFFER B-TYPE 1 ORTHOGONAL POLYNOMIAL SEQUENCES
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| Title | THE SHEFFER B-TYPE 1 ORTHOGONAL POLYNOMIAL SEQUENCES |
| Author | Galiffa, Daniel
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| Keywords | Sheffer
B-Type
Orthogonal polynomials
Characterizations
Three-term recurrence relation
Generating functions
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| Abstract | In 1939, I.M. Sheffer proved that every polynomial sequence belongs to one and only one $type$. Sheffer extensively developed properties of the $B$-\emph{Type 0} polynomial sequences and determined which sets are also orthogonal. He subsequently generalized his classification method to the case of arbitrary $B$-\emph{Type k} by constructing the generalized generating function $A(t)\mathrm=\sum_^\infty$, with $H_i(t)=h_t^i+h_t^+\cdots, \phantomh_\neq 0$. Although extensive research has been done on characterizing polynomial sequences, no analysis has yet been completed on sets of type one or higher ($k\geq1$). We present a preliminary analysis of a special case of the $B$-\emph{Type 1} ($k=1$) class, which is an extension of the $B$-\emph{Type 0} class, in order to determine which sets, if any, are also orthogonal sets. Lastly, we consider an extension of this research and comment on future considerations. In this work the utilization of computer algebra packages is indispensable, as computational difficulties arise in the $B$-\emph{Type 1} class that are unlike those in the $B$-\emph{Type 0} class. |
| Adviser | Ismail, Mourad
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| Publisher | University of Central Florida |
| Degree | Ph.D.
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| Degree Discipline | Department of Mathematics
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| Degree Grantor | Sciences
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| Degree Program | Mathematics PhD
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| Graduation Date | 2009-01-01 |
| Type | Doctoral dissertation
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| Access Level | Public - Allow Worldwide Access
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| Release Date | 2009-05-21 |
| Repository | University Archives
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| Repository Collection | Electronic Theses and Dissertations
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| Identifier | CFE0002551 |
| Access Link | http://purl.fcla.edu/fcla/etd/CFE0002551 |
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