Logaritma Fonksiyonunun İrrasyonel Fonksiyon İle Temsili ve Bu TemsileDayalı Üstel Fonksiyon Elde Edilmesi Üzerine

Bu çalışmada matematikte çok yaygın bir kullanım alanına sahip olan en temel fonksiyonlardan olan logaritma fonksiyonununirrasyonel bir fonksiyon ile temsil edilmesi üzerine çalışılmıştır. Bu amaçla logaritma fonksiyonu yerine kullanılabilecek irrasyonel birfonksiyon önerisi yapılmış, uygun matematik ve nümerik analiz tanım ve yöntemleri çerçevesinde önerilen fonksiyon elde edilmiştir.Elde edilen irrasyonel fonksiyon üzerinden ters fonksiyonu oluşturulmak suretiyle üstel fonksiyonlar için yeni bir yaklaşım eldeedilmiştir. Sayısal sonuçlar ve grafikler elde edilerek gerekli değerlendirmeler yapılmıştır.

On the Representation of the Logarithm Function by the Irrational Function and the Obtaining of an Exponential Function Based on This Representation

In this study, the representation of the logarithm function, which is one of the most basic functions that has a very common usage areain mathematics, has been studied with an irrational function. For this purpose, an irrational function that can be used instead of alogarithm function has been proposed, and the proposed function has been obtained within the framework of appropriate mathematicaland numerical analysis definitions and methods. A new approach has been obtained for exponential functions by constructing the inversefunction on the obtained irrational function. Necessary evaluations were made by obtaining numerical results and graphics.

PDF

___

Aleksandrov, A. G., (2014). Residues of Logarithmic Differential Forms in Complex Analysis and Geometry, Analysis in Theory and Applications, Vol. 30, No. 1, 34-50.
Andrews G. E., Askey R., Roy R. (1999). Special Functions, Encyclopedia of Mathematics and its Applications, 71, Cambridge University Press
Boyer, C. B. and Merzbach, U. C. (1991). Invention of Logarithms., A History of Mathematics, 2nd ed. New York: Wiley, 312-313.
Bruce, I., (2000), Napier’s logarithms., American Journal of Physics, 68(2):148–154
Fauvel, J., (2000). John Napier 1550–1617. EMS Newsletter, 38:24–25, (Reprinted pp. 1, 6–8 of CMS Notes-Notes de la SMC, volume 33, issue 6, October 2001)
Gautschi, W. (2008). On Euler’s attempt to compute logarithms by interpolation: A commentary to his letter of February 16, 1734 to Daniel Bernoulli, Journal of Computational and Appllied Mathematics, 219, no.2, 408-415.
Havil, J. (2003). The Baron's Wonderful Canon., 1.2 in Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, 4-11.
Kathleen, M., Montelle, C., (2015). Logarithms: The Early History of a Familiar Function - John Napier Introduces Logarithms, Mathematical Association of America.
Kreyszig E. (1993). Advanced Engineering Mathematics, John Wiley & Sons, 7th Edition.
Matala-Aho T., Vaananen Keijo, Zudilin Wadim. (2005). New Irrationality Measures for q-Logarithms, Mathematics of Computation, v. 75, Number 254, 879-889.
Mathews J. H. (1992). Numerical Methods for Mathematics, Science and Engineering, Prentice-Hall Inc., 2nd Ed.
Koelink, E., Assche, W. V. (2009). Leonhard Euler and a qanalogue of the logarithm. , American Mathematical Society, v.137, n.5, 1663-1676.
Nofal, C. P. (2006) Proof that the Natural Logarithm Can Be Represented by the Gaussian Hypergeometric Function. Pol D., (2018), On the values of logarithmic residues along curves, Ann. Inst. Fourier Grenoble, 68, 2, 725-766.
Rice B., Gonzales-Velasco E., Corrigan A. (2017). John Napier. In The Life and Works of John Napier, Springer.
Tajima. S., Nabeshima, K., (2021). Computing Regular Meromorphic Differential Forms via Saito’s Logarithmic Residues, Symmetry, Integrability and Geometry: Methods and Applications, Sigma 17.
Thomas, G. B., Maurice D. W., Joel H. R. (2010). Thomas’ Calculus, 12th Edition, Pearson.