TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Freq.: MONTHLY - Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Numerical approximation in real domain of special function of product of a variable and its double exponential

*

* Corresponding author · click or hover a name for details

pp. 1295–1318Vol. 27Issue 6September 2024DOI: 10.47974/JIM-1753XML
Received:
14 Jun 2023
Published Online:
30 Sep 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-1753
Pages:
1295–1318

Abstract

Purpose of writing this paper is to solve a transcendental  function containing product of a variable and its double exponential by a  unique method of approximation. If the value of the said product is given, then its inverse function is approximated by use of linear expression in place of natural logarithm of a positive real quantity and that transforms the function to a quadratic equation. Roots of the equation are, then used for solving the function. For precise approximation, the process is iterated a number of times and more the number of iterations, more precise will be the approximation. To prove precision of the formulae derived, a number of examples are given in tabular form.

Keywords

Subject Classifications

33E2033F05

References

[1] Fischer, M. J., and Michael O. Rabin, Super-Exponential Complexity of Presburger Arithmetic. Archived 2006-09-15 at the Wayback Machine, Proceedings of the SIAM-AMS Symposium in Applied Mathematics Vol. 7: pp 27–41 (1974).
[2] Kouznetsov, D.; Bisson, J.-F.; Li, J.; Ueda, K. Self-pulsing laser as oscillator Toda: Approximation through elementary functions, Journal of Physics A, 40 (9): pp 1–18 (2007), Bibcode:2007JPhA...40.2107K, doi:10.1088/1751-8113/40/9/016.
[3] Miller, J. C. P.; Wheeler, D. J. (1951), Large prime numbers, Nature, 168 (4280): 838 (1951), Bibcode: 1951Natur.168..838M, doi:10.1038/168838b0. 
[4] Nielsen, Pace P. (2003), An upper bound for odd perfect numbers, INTEGERS: The Electronic Journal of Combinatorial Number Theory, 3: A14 (2003).
[5] Pikhurko, Oleg, Lattice points in lattice polytopes, Mathematika, 48 (1–2): pp 15–24, arXiv:math/0008028, Bibcode:2000math......8028P, doi:10.1112/s0025579300014339.
[6] Varfolomeyev, S. D.; Gurevich, K. G., The hyperexponential growth of the human population on a macrohistorical scale, Journal of Theoretical Biology, 212 (3): pp 367-372 (2011), doi:10.1006/jtbi.2001.2384, PMID 11829357.
[7] Wadhawan, N. K., Wadhawan, P., Approximation Of Logarithm, Factorial And Euler-Mascheroni Constant Using Odd Harmonic Series, Mathematical Forum, 28(2), pp 125-144 (2020), http://mathematical-forum.org/wp-content/uploads/2021/07/10.-MF592020.pdf. 
[8] Wikipedia, Newton’s Method at https://en.m.wikipedia.org/wiki/Newton’s_method#Failure_analysis.

Views: 105Downloads: 6Citations: 0