This paper provides closed-form formulas for coefficients of convergents of some popular continued fraction expansions (CFEs) approximating $s^{\nu}$, with $-1<\nu<1$, and $(2/T)^{\nu}((z-1)/(z+1))^{\nu}$. The expressions of the coefficients are given in terms of $\nu$ and of the degree $n$ of the polynomials defining the convergents. The formulas greatly reduce the effort for approximating fractional operators and show the equivalence between two well-known CFEs in a given condition.

Closed-form rational approximations of fractional, analog and digital differentiators/integrators / Maione, Guido. - In: IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN CIRCUITS AND SYSTEMS. - ISSN 2156-3357. - 3:3(2013), pp. 322-329. [10.1109/JETCAS.2013.2268949]

Closed-form rational approximations of fractional, analog and digital differentiators/integrators

MAIONE, Guido
2013-01-01

Abstract

This paper provides closed-form formulas for coefficients of convergents of some popular continued fraction expansions (CFEs) approximating $s^{\nu}$, with $-1<\nu<1$, and $(2/T)^{\nu}((z-1)/(z+1))^{\nu}$. The expressions of the coefficients are given in terms of $\nu$ and of the degree $n$ of the polynomials defining the convergents. The formulas greatly reduce the effort for approximating fractional operators and show the equivalence between two well-known CFEs in a given condition.
2013
Closed-form rational approximations of fractional, analog and digital differentiators/integrators / Maione, Guido. - In: IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN CIRCUITS AND SYSTEMS. - ISSN 2156-3357. - 3:3(2013), pp. 322-329. [10.1109/JETCAS.2013.2268949]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/1541
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