Abstract
Asymptotic approximations of Tangent polynomials, Tangent-Bernoulli, and Tangent-Genocchi polynomials are derived using saddle point method and the approximations are expressed in terms of hyperbolic functions. For each polynomial there are two approximations derived with one having enlarged region of validity.
Highlights
IntroductionSeveral well-known special functions, numbers and polynomials (e.g. zeta functions, Bernoulli, Euler and Genocchi numbers and polynomials and derivative polynomials [1,2,3,4,5,6]) have been studied by many researchers in recent decade due to their wide-ranging applications from number theory and combinatorics to other fields of applied mathematics
Several well-known special functions, numbers and polynomials have been studied by many researchers in recent decade due to their wide-ranging applications from number theory and combinatorics to other fields of applied mathematics
Some variations are constructed by mixing the concept of two special functions, numbers or polynomials
Summary
Several well-known special functions, numbers and polynomials (e.g. zeta functions, Bernoulli, Euler and Genocchi numbers and polynomials and derivative polynomials [1,2,3,4,5,6]) have been studied by many researchers in recent decade due to their wide-ranging applications from number theory and combinatorics to other fields of applied mathematics. Different variations and generalizations of these functions, numbers and polynomials have been constructed and investigated. Some variations are constructed by mixing the concept of two special functions, numbers or polynomials. The Apostol-Genocchi polynomials, Frobenius-Euler polynomials, Frobenius-Genocchi polynomials and Apostol-Frobenius-type poly-Genocchi polynomials in [12,13,14] are constructed by mixing the concepts of Apostol, Frobenius, Genocchi and Euler polynomials Another interesting mixture of special polynomials can be constructed by joining the concept of Tangent polynomials with Bernoulli and Genocchi polynomials. The. Tangent polynomials TnðzÞ, Tangent – Bernoulli ðTBÞnðzÞ and Tangent – Genocchi ðTGÞnðzÞ polynomials are defined by the generating functions. The Tangent polynomials, Tangent-Bernoulli, and Tangent-Genocchi polynomials will be given asymptotic approximations using the method used in [19, 20]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
