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Matrix continued fraction expansion of Bessel function

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

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.




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

Abstract

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.
There are 10 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ali Kacha This is me

Gul Karadeniz Gozeri This is me

Kacem Belhroukia This is me

Publication Date September 30, 2016
Published in Issue Year 2016 Volume: 4 Issue: 3

Cite

APA Kacha, A., Gozeri, G. K., & Belhroukia, K. (2016). Matrix continued fraction expansion of Bessel function. New Trends in Mathematical Sciences, 4(3), 1-8.
AMA Kacha A, Gozeri GK, Belhroukia K. Matrix continued fraction expansion of Bessel function. New Trends in Mathematical Sciences. September 2016;4(3):1-8.
Chicago Kacha, Ali, Gul Karadeniz Gozeri, and Kacem Belhroukia. “Matrix Continued Fraction Expansion of Bessel Function”. New Trends in Mathematical Sciences 4, no. 3 (September 2016): 1-8.
EndNote Kacha A, Gozeri GK, Belhroukia K (September 1, 2016) Matrix continued fraction expansion of Bessel function. New Trends in Mathematical Sciences 4 3 1–8.
IEEE A. Kacha, G. K. Gozeri, and K. Belhroukia, “Matrix continued fraction expansion of Bessel function”, New Trends in Mathematical Sciences, vol. 4, no. 3, pp. 1–8, 2016.
ISNAD Kacha, Ali et al. “Matrix Continued Fraction Expansion of Bessel Function”. New Trends in Mathematical Sciences 4/3 (September 2016), 1-8.
JAMA Kacha A, Gozeri GK, Belhroukia K. Matrix continued fraction expansion of Bessel function. New Trends in Mathematical Sciences. 2016;4:1–8.
MLA Kacha, Ali et al. “Matrix Continued Fraction Expansion of Bessel Function”. New Trends in Mathematical Sciences, vol. 4, no. 3, 2016, pp. 1-8.
Vancouver Kacha A, Gozeri GK, Belhroukia K. Matrix continued fraction expansion of Bessel function. New Trends in Mathematical Sciences. 2016;4(3):1-8.