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

Author

Listed:
  • Ali Hamzah Alibrahim

    (Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, Penryn Campus, Penryn TR10 9FE, UK
    Mathematics Department, College of Science, Jouf University, Sakaka 2014, Saudi Arabia)

  • Saptarshi Das

    (Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, Penryn Campus, Penryn TR10 9FE, UK
    Institute for Data Science and Artificial Intelligence, University of Exeter, North Park Road, Exeter EX4 4QE, UK)

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.

Suggested Citation

  • Ali Hamzah Alibrahim & Saptarshi Das, 2024. "Bridging the p -Special Functions between the Generalized Hyperbolic and Trigonometric Families," Mathematics, MDPI, vol. 12(8), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1242-:d:1379170
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