Generalized Binomial Convolution of the mth Powers of the Consecutive Integers with the General Fibonacci Sequence

Abstract

In this paper, we consider Gauthier’s generalized convolution and then define its binomial analogue as well as alternating binomial analogue. We formulate these convolutions and give some applications of them.

Keywords

• binomial convolution
• general Fibonacci sequence
• Stirling numbers of the second kind