Cycle indicators and special functions. (English) Zbl 0987.05007

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.


05A15 Exact enumeration problems, generating functions
05A17 Combinatorial aspects of partitions of integers
11B37 Recurrences
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B83 Special sequences and polynomials
12E10 Special polynomials in general fields
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