Infinitely Differentiable Generalized Logarithmic and Exponential Functions

DOI10.2307/2938713zbMath0742.39005OpenAlexW4255790377MaRDI QIDQ3980476

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Publication date: 26 June 1992

Full work available at URL: https://doi.org/10.2307/2938713

zbMATH Keywords

iterative proceduregeneralized exponential functionsinfinitely differentiable solutionsgeneralized logarithmic function

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Iteration theory, iterative and composite equations (39B12) Other special functions (33E99)

Related Items (7)

The prompter method: a treatment for hard-to-solve iterative functional equations ⋮ Solving \(F(z+1)=b^{F(z)}\) in the complex plane ⋮ A new class of distributions on the whole real line based on the continuous iteration approach ⋮ Uniqueness of holomorphic Abel functions at a complex fixed point pair ⋮ Portrait of the four regular super-exponentials to base sqrt(2) ⋮ Solution of $F(z+1)=\exp \big (F(z)\big )$ in complex $z$-plane ⋮ Abel's functional equation and eigenvalues of composition operators on spaces of real analytic functions

Cites Work

• Unnamed Item
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• On the solutions of an Abelian functional equation
• Tables of the logaritm of iteration of e^x—1
• The Exponential of Iteration of e x - 1
• Dynamics of exp (z)
• A Class of functional equations which have entire solutions

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