Matrix continued fraction expansion of Bessel function

Year 2016, Volume: 4 Issue: 3, 1 - 8, 30.09.2016

Ali Kacha Gul Karadeniz Gozeri Kacem Belhroukia

https://izlik.org/JA98ML64RJ

Abstract

The aim of this paper is to provide some results and
applications of continued fractions with matrix arguments. First, we recall
some properties of matrix functions with real coefficients. Afterwards, we give
a matrix continued fraction expansion of the Bessel function.

Keywords

Continued fraction expansion , positive definite matrix , matrix continued fraction , development of series

References

• T. Ando, Topics on operators inequalities, Ryukyu Univ. Lecture note Series 1, 1978.
• A.Cuyt, V.Brevik Petersen, Handbook of continued fractions for special functions, Springer (2007).
• F. R.Gantmacher. The Theory of Matrices, Vol. I. Chelsa, New York, Elsevier Science Publishers, (1992).
• V. Gen H.Golub and Charles F.Van Loan, Matrix Computations, Johns Hopking University Press, Baltimore, MD, USA, third edition (1996).
• T. L. HAYDEN, Continued fractions in Banach spaces, Rocky Mtn. J.Math., 4 (1974), pp. 367-369.
• A.N, Khovanski, The applications of continued fractions and their Generalisation to problemes in approximation theory,1963, Noordhoff, Groningen, The Netherlands (chap2).
• L.Lorentzen, H.Wadeland, Continued fractions with application, Elseiver Science Publishers, (1992).
• Gerard J. MURPHY, C^*-Algebras and operators theory, (1990), Academic press, INC Harcourt Brace Jovanovich, publishers.
• N. NEGOESCU, Convergence theorems on noncommutative continued fractions, Rev. Anal. Numér. Théorie Approx., 5 (1977), pp. 165-180.
• M.Raissouli, A.Kacha, Convergence for matrix continued fractions. Linear Algebra and its Applications, 320 (2000), pp. 115-129.