Some identities on degenerate hyperbolic functions arising from $ p $-adic integrals on $ mathbb{Z}_p $

Some identities on degenerate hyperbolic functions arising from $ p $-adic integrals on $ mathbb{Z}_p $

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The aim of this paper is to Intake Kit introduce several degenerate hyperbolic functions as degenerate versions of the hyperbolic functions, to evaluate Volkenborn and the fermionic $ p $-adic integrals of the degenerate hyperbolic cosine and the degenerate hyperbolic sine functions and to derive from them some identities ONE NATURAL involving the degenerate Bernoulli numbers, the degenerate Euler numbers and the Cauchy numbers of the first kind.