# Ultra power and ultra exponential functions

@article{Hooshmand2006UltraPA, title={Ultra power and ultra exponential functions}, author={M. H. Hooshmand}, journal={Integral Transforms and Special Functions}, year={2006}, volume={17}, pages={549 - 558} }

Supposing that a is a positive real number, then for each natural number n, the notation a n is called a to the ultra power of n , and we define by In the other words, , n times. In [Euler, L., De formulis exponentialibus replicatus, Acta Academiac Petropolitenae, 1, 38–60.] the necessary and sufficient condition for the convergence of lim n→∞ a n is proved by Euler and in [Baker, I.N. and Rippon, P.J., 1983, Convergence of infinite exponentials. Annales Academiac Scentiarium Fennicae…

## 18 Citations

Infra logarithm and ultra power part functions

- Mathematics
- 2008

Considering the serial operations as multiplication and power, we introduced the next step of them in [M.H. Hooshmand, Ultra power and ultra exponential functions, Integral Transforms Spec. Funct. 17…

Ultra power of higher orders and ultra exponential functional sequences

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- 2018

Abstract The word tetration (was coined by Reuben Louis Goodstein) is the next hyper operator after exponentiation, and is defined as iterated exponentiation. The first uniqueness theorem for…

On the Arithmetic of Knuth's Powers and Some Computational Results About Their Density

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The object of the paper is the so-called “unimaginable numbers”, and some arithmetic and computational aspects of the Knuth’s powers notation are dealt with and some first steps into the investigation of their density are moved into.

ON SMOOTH SOLUTIONS OF NON LINEAR

- Mathematics
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We consider the dynamical system, fn+1 = u(fn), (1) (where usually n, is time) defined by a cont inuous map u. Our target is to find a flow of the system for ea ch initial state f0, i.e., we seek…

Ackermann functions of complex argument

- Mathematics
- 2008

Institute for Laser Science, University of Electro-Communications 1-5-1Chofu-Gaoka, Chofu, Tokyo, 182-8585, JapanAbstractExistence of analytic extension of the fourth Ackermann function A(4,z) to…

Functions of ultraexponential and infralogarithm types and general solution of the Abel functional equation

- Mathematics
- 2011

We propose generalized forms of ultraexponential and infralogarithm functions introduced and studied earlier by the author and present two classes of special functions, namely, ultraexponential and…

Limit summability of ultra exponential functions

- Mathematics, Philosophy
- 2012

In [1] we uniquely introduced ultra exponential functions (uxpa) and defined next step of the serial binary operations: addition, multiplication and power. Also, we exhibited the topic of limit…

ON SMOOTH SOLUTIONS OF NON LINEAR DYNAMICAL SYSTEMS, fn+1 = u(fn), PART I

- Mathematics
- 2014

We consider the dynamical system, fn+1 = u(fn), (1) (where usually n, is time) defined by a continuous map u. Our target is to find a flow of the system for each initial state f0, i.e., we seek…

Solution of F(z+1)=exp(F(z)) in complex z-plane

- MathematicsMath. Comput.
- 2009

Robusts of the convergence and smallness of the residual indicate the existence of unique tetration F(z), that grows along the real axis and approaches L along the imaginary axis, being analytic in the whole complex z-plane except for singularities at integer the z ― 1 and the cut at z < ―2.

Paradoxes of the Infinite and Ontological Dilemmas Between Ancient Philosophy and Modern Mathematical Solutions

- PhilosophyNUMTA
- 2019

The present work illustrates the ontological and epistemological nature of the paradoxes of the infinite, focusing on the theoretical framework of Aristotle, Kant and Hegel, and connecting theEpistemological issues about the infinite to concepts such as the continuum in mathematics.

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