#### Title

On the Construction of Number Sequence Identities

#### Abstract

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.

#### Disciplines

Mathematics

#### Recommended Citation

He, Tian-Xiao and Chou, Wun-Seng, "On the Construction of Number Sequence Identities" (2013). *Scholarship*. 3.

https://digitalcommons.iwu.edu/math_scholarship/3

## Comments

The

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