A New Type of Generalized Ernst Numbers

Abstract

This study presents, the Gaussian generalized Ernst numbers as a new complex recursive number sequence. We also give Binet's formulas, Simson's formulas, generating functions for this sequence and we touch on Gaussian Ernst and Gaussian Ernst-Lucas numbers. Besides,we establish some identities and matrices associated with these sequences. This study's contribution to the literature is the constructed of an important generalization of generalized Ernst numbers that can be applied to different fields and the establishment of important equations regarding these numbers.

Keywords

• Ernst numbers
• Gaussian Ernst numbers
• Gaussian Ernst-Lucas numbers;
• Gaussian generalized Ernst numbers.

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