On the Construction of Number Sequence Identities

Publication Date

January 2013


The Journal of Concrete and Applicable Mathematics is published by Eudoxus Press, LLC., http://www.msci.memphis.edu/~ganastss/jcaam/.


To construct a class of identities for number sequences generated by linear recurrence relations. An alternative method based on the generating functions of the sequences is given. The equivalence between two methods for linear recurring sequences are also shown. However, the second method is not limited to the linear recurring sequences, which can be used for a wide class of sequences possessing rational generating functions. As examples, Many new and known identities of Stirling numbers of the second kind, Pell numbers, Jacobsthal numbers, etc., are constructed by using our approach. Finally, we discuss the hyperbolic expression of the identities of linear recurring sequences.



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