Prabhakar, Supertrigonometric, and Superhyperbolic Functions

Xiao-Jun Yang ()
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Xiao-Jun Yang: China University of Mining and Technology, School of Mathematics and State Key Laboratory for Geomechanics and Deep Underground Engineering

Chapter Chapter 5 in Theory and Applications of Special Functions for Scientists and Engineers, 2021, pp 499-645 from Springer

Abstract: Abstract In this chapter, we introduce the Prabhakar function and propose the supertrigonometric and superhyperbolic functions via Prabhakar function. The Laplace transforms for the new special functions and integral representations for the supertrigonometric and superhyperbolic functions are discussed in detail. The truncated Prabhakar, supertrigonometric, and superhyperbolic functions are proposed, and the general fractional calculus involving the Prabhakar function is also considered. Finally, the integral equations and mathematical models related to Prabhakar function are presented.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-33-6334-2_5

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DOI: 10.1007/978-981-33-6334-2_5

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