Julia and Mandelbrot Sets of the Gamma Function Using Lanczos Approximation
Applied and Computational Mathematics
Volume 5, Issue 2, April 2016, Pages: 73-77
Received: Mar. 20, 2016; Accepted: Mar. 29, 2016; Published: Apr. 15, 2016
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Authors
Richard Eneojo Amobeda, Department of Mathematics, Kogi State College of Education (Technical), Kabba, Nigeria
Terhemen Aboiyar, Department of Mathematics/Statistics/Computer Science, University of Agriculture, Makurdi, Nigeria
Solomon Ortwer Adee, Department of Mathematics, Modibbo Adama University of Technology, Yola, Nigeria
Peter Vanenchii Ayoo, Department of Mathematics, Federal University Lafia, Nigeria
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Abstract
This work explores the Julia and Mandelbrot sets of the Gamma function by extending the function to the entire complex plane through analytic continuation and functional equations. Various Julia and Mandelbrot sets associated with the Gamma function are generated using the iterative function , with different parameter values. To produce an accurate result using the integral definition of the Gamma function, a large number of terms would have to be added during the numerical integration procedure; this makes computation of Gamma function a very difficult task. To overcome this challenge, the Lanczos approximation of the Gamma function which presents an efficient and easy way to compute algorithms for approximating the Gamma function to an arbitrary precision is used. The resulting images reveal that the fractal (chaotic) behaviour found in elementary functions is also found in the Gamma function. The chaotic nature of the Julia and Mandelbrot sets provides a way of understanding complexity in systems as well as just in shapes.
Keywords
Julia Set, Mandelbrot Set, Gamma Function, Lanczos Approximation, Complex Functions
To cite this article
Richard Eneojo Amobeda, Terhemen Aboiyar, Solomon Ortwer Adee, Peter Vanenchii Ayoo, Julia and Mandelbrot Sets of the Gamma Function Using Lanczos Approximation, Applied and Computational Mathematics. Vol. 5, No. 2, 2016, pp. 73-77. doi: 10.11648/j.acm.20160502.16
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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