Closed formulas for computing higher-order derivatives of functions involving exponential functions

DOI10.1016/j.amc.2015.08.051zbMath1410.33002OpenAlexW1120565459MaRDI QIDQ670771

Aimin Xu, Zhongdi Cen

Publication date: 20 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.08.051

zbMATH Keywords

trigonometric functionclosed formulahyperbolic functionhigher-order derivativetangent number

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Combinatorial identities, bijective combinatorics (05A19) Exponential and trigonometric functions (33B10)

Related Items (8)

Special values of the Bell polynomials of the second kind for some sequences and functions ⋮ Derivative polynomials of a function related to the Apostol-Euler and Frobenius-Euler numbers ⋮ A diagonal recurrence relation for the Stirling numbers of the first kind ⋮ Simplifying differential equations concerning degenerate Bernoulli and Euler numbers ⋮ An explicit formula for derivative polynomials of the tangent function ⋮ On the higher derivatives of the inverse tangent function ⋮ Unnamed Item ⋮ Closed formulas and identities on the Bell polynomials and falling factorials.

Cites Work

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• Some identities and an explicit formula for Bernoulli and Stirling numbers
• Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind
• On Ruijsenaars' asymptotic expansion of the logarithm of the double gamma function
• Some identities involving exponential functions and Stirling numbers and applications
• Tangent numbers and operators
• Diagonal recurrence relations, inequalities, and monotonicity related to the Stirling numbers of the second kind
• Permutations, Sequences and Special Functions
• Derivative Polynomials for Tangent and Secant
• Derivative Polynomials for tanh, tan, sech and sec in Explicit Form

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