We study some ratios related to hyper-Horadam numbers such as Wnr/Wn-1r while n→∞ by using a symmetric algorithm obtained by the recurrence relation ank=ank-1+an-1k, where Wnr is the nth hyper-Horadam number. Also, we give some special cases of these ratios such as the golden ratio and silver ratio.

Abstract. In this paper, we study norms of circulant matrices F = Circ(F

Abstract. In this paper, we study norms of circulant matrices H = Circ(H

In this paper, we compute the spectral norms of r− circulant matrices with the hyper-Fibonacci and hyper-Lucas numbers of the forms) and their Hadamard and Kronecker products. For this, we firstly compute the spectral and Euclidean norms of circulant matrices of the forms. Moreover, we give some examples related to special cases of our results.

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The aim of this paper is to define hyper-Leonardo hybrinomials as a generalization of the Leonardo Pisano hybrinomials and to examine some of their properties such as the recurrence relation, summation formula and generating function. Another aim is to introduce hyper hybrid-Leonardo numbers.

Highlights• We define hyperbolic Horadam functions.• We present their hyperbolic and recursive properties.• Our findings generalize the previous studies.

In this paper, we introduce a new generalization for the gamma function as hyper-gamma function. Some identities and integral representation are obtained for the this new generalization.