On compact explicit formulas of the partial fraction decomposition and applications
DOI:
https://doi.org/10.22481/intermaths.v4i1.12294Resumo
This study concerns another approach for computing the scalars Ai(k) of the partial fraction decomposition ... Some illustrative special cases and several examples are furnished, to show the efficiency of this new approach. Finally, concluding remarks and perspectives are presented.
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Abel, U., Applications of a Generalized Leibniz Rule, Constructive Theory of Functions,
Sozopol 2013 (K. Ivanov, G. Nikolov and R. Uluchev, Eds.), pp. 1-9 Prof. Marin Drinov
Academic Publishing House, Sofia, 2014.
Ben Taher, R. and Rachidi, M., Explicit formulas for the constituent matrices. Application to the matrix functions, Special Matrices, Volume 3, Issue: 1 (2015), page 43-52.
https://doi.org/10.1515/spma-2015-0004
Bradley, W. T. and Cook, W. J., Two Proofs of the Existence and Uniqueness of the
Partial Fraction Decomposition, International Mathematical Forum, Vol. 7, 2012, no. 31,
-1535.
Henrici, P., Applied ans computational complex analysis, Vol. 1 , John Wiley & Sons, New
York.London. Sydney.Toronto, 1974. https://doi.org/10.1002/zamm.19770570622
Kim, Y. and Lee, B. (2016) Partial Fraction Decomposition by Repeated Synthetic Division. American Journal of Computational Mathematics, 6, 153-158.
http://dx.doi.org/10.4236/ajcm.2016.62016
Kung, Sidney H., Partial Fraction Decomposition by Division, The College Mathematics
Journal, Vol. 37, No. 2 (Mar., 2006), pp. 132134
Man, Y.K. (2012) A Cover-Up Approach to Partial Fractions with Linear or Irreducible
Quadratic Factors in the Denominators. Applied Mathematics and Computation, 219,
-3862. http://dx.doi.org/10.1016/j.amc.2012.10.016
Majumdar, R., Generalization of Pascal’s Rule and Leibniz’s Rule for Differentiation, RoseHulman Undergraduate Mathematics Journal, Vol. 18 Iss. 1 (2017), Article 12. Available
at: https://scholar.rose-hulman.edu/rhumj/vol18/iss1/12
Man, Yiu-K., A simple algorithm for computing partial fraction expansions with multiple
poles, International Journal of Mathematical Education in Science and Technology, 38:2
(2007), 247-251. https://doi.org/10.1080/00207390500432337
Nicholson, W.K., Introduction to Abstract Algebra, Boston: PWS Publishing, 1993.
Norman, L.B., Discrete Mathematics, , 2nd edn, New York: Oxford University Press, 1990.
Rose, D.A. Partial Fractions by Substitution. The College Mathematics Journal, 38 (2007),
-147.
Sloła, D. and Wituła, R., Three Bricks Method of the Partial Fraction Decomposition
of Some Type of Rational Expression. Lecture Notes in Computer Science, 3516 (2005),
-662. http://dx.doi.org/10.1007/11428862_89
Wituła, R. and Słota, D., Partial Fractions Decomposition of Some Rational Functions. Applied Mathematics and Computation, 197 (2008), 328-336.
http://dx.doi.org/10.1016/j.amc.2007.07.048
Ma, Y., Yu, J. and Wang, Y., Efficient Recursive Methods for Partial Fraction Expansion
of General Rational Functions. Journal of Applied Mathematics, 2014, Article ID: 895036.
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