Journals / Results in Nonlinear Analysis / 2020 / Cilt: 3 - Sayı: 4
Three closed forms for convolved Fibonacci numbers
- Pages
- 185–195
- DOI
- —
Abstract
In the paper, by virtue of the Fa\`a di Bruno formula and several properties of the Bell polynomials of the second kind, the author computes higher order derivatives of the generating function of convolved Fibonacci numbers and, consequently, derives three closed forms for convolved Fibonacci numbers in terms of the falling and rising factorials, the Lah numbers, the signed Stirling numbers of the first kind, and the golden ratio. In the paper, by virtue of the Fa\`a di Bruno formula and several properties of the Bell polynomials of the second kind, the author computes higher order derivatives of the generating function of convolved Fibonacci numbers and, consequently, derives three closed forms for convolved Fibonacci numbers in terms of the falling and rising factorials, the Lah numbers, the signed Stirling numbers of the first kind, and the golden ratio. ; ; ; ; ;