Document Type : Research Paper

Authors

• Ramdoss Murali ¹
• Veeramani Vithya ¹
• Choonkil Park ²

¹ Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur 635 601, Tamil Nadu, India

² Research Institute for Convergence of Basic Science, Hanyang University, Seoul 04763, Korea

Abstract

In this research work, we define a tetranacci function $\zeta: \mathbb{R}\to \mathbb{R}$  satisfying
$$\zeta(4+\omega) = \zeta (3+\omega) + \zeta (2+\omega)+ \zeta (1+\omega)+ \zeta (\omega),$$
for all $\omega \in \mathbb{R}$.  We apply induction technique to obtain useful results for tetranacci functions with tetranacci numbers and also prove that $\lim \limits_{\omega \rightarrow \infty} \frac{\zeta(\omega+1)}{\zeta(\omega)} = \delta >1$, where $\delta$  is one of the zeros of the equation $\omega^{4} - \omega^{3} - \omega^{2} - \omega -1 = 0$.

Keywords

• Tetranacci number
• Tetranacci function
• Quotient of tetranacci functions
• Induction method