논문KCI 등재
CONTINUED FRACTION REPRESENTATIONS OF THE INCOMPLETE GAMMA FUNCTION
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In this paper, we summarize the basic definitions and results of matrices, matrix functions, and continued fractions. In the convergent case, the continued fractions expansions have the advantage that they converge more rapidly than other numerical algorithms. Further, this article aims to give a continued fraction expansion of the incomplete gamma function.
Abstract
In this paper, we summarize the basic definitions and results of matrices, matrix functions, and continued fractions. In the convergent case, the continued fractions expansions have the advantage that they converge more rapidly than other numerical algorithms. Further, this article aims to give a continued fraction expansion of the incomplete gamma function.
참고문헌 (12)
- M. Abramowitz, "Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables" (1965), Dover Publications, INC
- A. Cuyt, "Handbook of Continued Fractions for Special Functions" (2007), Springer
- N. J. Higham, "Functions of Matrices: Theory and Computations" (2008), SIAM Publications Library
- W. Gautschi, "The incomplete gamma functions ince Tricomi, in: Tricomi’s Ideas and Contemporary Applied Mathematics", AttiConv. Lincei, Accad. Naz. Lincei, Rome, 147, pp.203~237 (1998)
- G. H. Golub, "Matrix computations" (2013), Johns Hopkins University Press
- W. B. Jones, "Continued Fractions: Analytic Theory and Applications" (1980), Addisson-Wesley, Cambridge University Press
- A. N. Khovanskii, "The Application of continued fractions and their generalizations to problems in approximation theory" (1963)
- L. Lorentzen, "Continued fractions with applications, 3" (1992)
- G. J. Murphy, "C∗-algebra and operator theory" (1990), Academic Press, Inc
- N. Negoescu, "Convergence theorems on noncommutative continued fractions", Rev. Anal. Num´e. Th´erie Approx, 5, pp.165~180 (1977)
- M. Raissouli, "Convergence of matrix continued fractions", Linear Algebra Appl, 320, pp.115~129 (2000)
- M. Sababheh, "Convexity and matrix means", Linear Algebra Appl, 506, pp.588~602 (2016)
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