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Mittag-Leffler, Supertrigonometric, and Superhyperbolic Functions

In: Theory and Applications of Special Functions for Scientists and Engineers

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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)

Abstract

In this chapter, we introduce the theory of the Mittag-Leffler function, supertrigonometric functions, and superhyperbolic functions. The integral representations for the Mittag-Leffler function and related functions are addressed and the general fractional calculus operators are also discussed in detail. The integral equations in the kernels of the Mittag-Leffler function, supertrigonometric functions, and superhyperbolic functions are presented; the truncated Mittag-Leffler, supertrigonometric, and superhyperbolic functions are considered; and some mathematical models are derived to explain the power-law behaviors in material science.

Suggested Citation

  • Xiao-Jun Yang, 2021. "Mittag-Leffler, Supertrigonometric, and Superhyperbolic Functions," Springer Books, in: Theory and Applications of Special Functions for Scientists and Engineers, chapter 0, pages 255-366, Springer.
    • Handle: RePEc:spr:sprchp:978-981-33-6334-2_3
    DOI: 10.1007/978-981-33-6334-2_3
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