Abstract
This work is aimed to obtain the complex partial fraction decompositions of rational functions. We express the coefficients of complex partial fraction decomposition of arbitrary rational functions in terms of the coefficients of their real partial fraction decomposition. This type of decompositions is then used to generalize the high order derivatives of such rational functions. Moreover, different applications are selected to demonstrate the applicability of introduced algorithms.
Highlights
Rational functions are widely used in many branches of mathematics such as numerical analysis i.e Pade Approximations, mathematical analysis as well as mathematical modelling and they appear in mathematical representations of many problems in science and engineering [1,2,3,4,5,6,7]
Long division, algorithms introduced in [1,2] can be used for suitable applications. These algorithms especially focus for determining the real partial fraction decomposition method (PFD) for given rational functions
Complex PFDs can effectively be used in the parts of suitable applications
Summary
Rational functions are widely used in many branches of mathematics such as numerical analysis i.e Pade Approximations, mathematical analysis as well as mathematical modelling and they appear in mathematical representations of many problems in science and engineering [1,2,3,4,5,6,7]. One of the famous and simplest methods is partial fraction decomposition method (PFD) for suitable applications: Consider a polinomial function Q(x) with real coefficients and recall that there exist some integers k1 ,..., kp ,l1 ,...,lq ≥ 1 such that. Assume that P(x) is another polynomial such that deg(P)
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