Bridging the p -Special Functions between the Generalized Hyperbolic and Trigonometric Families

Ali Hamzah Alibrahim and Saptarshi Das ()
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Ali Hamzah Alibrahim: Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, Penryn Campus, Penryn TR10 9FE, UK
Saptarshi Das: Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, Penryn Campus, Penryn TR10 9FE, UK

Mathematics, 2024, vol. 12, issue 8, 1-13

Abstract: Here, we study the extension of p -trigonometric functions sinp and cosp family in complex domains and p -hyperbolic functions sinhp and the coshp family in hyperbolic complex domains. These functions satisfy analogous relations as their classical counterparts with some unknown properties. We show the relationship of these two classes of special functions viz. p -trigonometric and p -hyperbolic functions with imaginary arguments. We also show many properties and identities related to the analogy between these two groups of functions. Further, we extend the research bridging the concepts of hyperbolic and elliptical complex numbers to show the properties of logarithmic functions with complex arguments.

Keywords: p -trigonometric functions; p -hyperbolic functions; p -complex logarithm; special functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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