**Title:** Formulas on Fibonacci type numbers and polynomials derived from linear recurrence relations and generating functions

**Montes Taurus J. Pure Appl. Math.** / ISSN: 2687-4814

**Article ID:** MTJPAM-D-23-00007; **Volume 5 / Issue 3 / Year 2023**, Pages 120-130

**Document Type:** Research Paper

**Author(s):** Yagmur Cetin ^{a} , Yilmaz Simsek ^{b}

^{a}Department of Mathematics, Faculty of Science University of Akdeniz TR-07058, Antalya-Turkey

^{b}Department of Mathematics, Faculty of Science University of Akdeniz TR-07058, Antalya-Turkey

Received: 4 April 2023, Accepted: 25 July 2023, Published: 3 September 2023.

**Corresponding Author:** Yagmur Cetin (Email address: yagmur48@gmail.com)

**Full Text:** PDF

**Abstract**

One of the purposes of this article is to investigate the solution of Exercise 7.7.11 of the Charalambides’s book [5, p. 267] and some properties of the generating functions derived from it. Comparisons of this generating function obtained from the result of this problem with other known generating functions are made. In addition to these, some new results are derived. Moreover, we give the generating function of a new family of special polynomials. We also give some properties of these polynomials associated with their derivatives and integrals. Finally, some new formulas involving the Fibonacci type numbers and polynomials, the Pell numbers, the combinatorial numbers, the Stirling numbers of the first kind, the Cauchy numbers and polynomials, and also finite sums are given.

**Keywords:** Generating functions, Fibonacci type numbers and polynomials, Pell numbers, Cauchy numbers and polynomials, finite sum, combinatorial numbers

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