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Cycle Indicators and Special Functions
Leetsch C. Hsu1 and Peter Jau-Shyong Shiue2
1Department of Mathematics, Dalian University of Technology, Dalian 116024, China
2Department of Mathematical Sciences, University of Nevada, Las Vegas, NV 89154-4020, USA
shiue@nevada.edu
Annals of Combinatorics 5 (2) p.179-196 June, 2001
AMS Subject Classification: 05A15, 05A17, 11B37, 11B39, 11B83, 12E10, 33C25
Abstract:
It is shown that a class of special functions (involving Sheffer-type polynomials and Gegenbauer-Humbert-type polynomials) could have cycle indicator representations and some recurrence relations. This implies the conclusion that classical special functions with simple logarithms of generating functions can be classified this way. This paper is mainly devoted to establish various relations and identities for special functions and remarkable number sequences.
Keywords: cycle indicator, -representation, -representablity

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