2. Author's Information
    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
  3. 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
    DOI: 10.11648/j.acm.20160502.16
    ADLID: 31004-v5
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  1. Keywords
    Julia Set Mandelbrot Set Gamma Function Lanczos Approximation Complex Functions
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