Inverse polynomial expansions of Laurent series, II
نویسندگان
چکیده
An algorithm is considered, and shown to lead to various unusual and unique series expansions of formal Laurent series, as the sums of reciprocals of polynomials. The degrees of approximation by the rational functions which are the partial sums of these series are investigated. The types of series corresponding to rational functions themselves are also partially characterized.
منابع مشابه
ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS
Let $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138-156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew inverseLaurent-serieswise Armendariz rings. In this article, we study on aspecial type of these rings and introduce strongly Armendariz ringsof inverse ske...
متن کاملA Natural Series for the Natural Logarithm
Rodriguez Villegas expressed the Mahler measure of a polynomial in terms of an infinite series. Lück’s combinatorial L-torsion leads to similar series expressions for the Gromov norm of a knot complement. In this note we show that those formulae yield interesting power series expansions for the logarithm function. This generalizes an infinite series of Lehmer for the natural logarithm of 4. 1 T...
متن کامل# a 7 Integers 11 B ( 2011 ) Subword Complexity and Laurent Series
Decimal expansions of classical constants such as √ 2, π and ζ(3) have long been a source of difficult questions. In the case of Laurent series with coefficients in a finite field, where “no carries appear,” the situation seems to be simplified and drastically different. In 1935 Carlitz introduced analogs of real numbers such as π, e or ζ(3) and it became reasonable to enquire how “complex” the...
متن کاملSubword Complexity and Laurent Series with Coefficients in a Finite Field
Decimal expansions of classical constants such as √ 2, π and ζ(3) have long been a source of difficult questions. In the case of Laurent series with coefficients in a finite field, where no carry-over difficulties appear, the situation seems to be simplified and drastically different. On the other hand, Carlitz introduced analogs of real numbers such as π, e or ζ(3). Hence, it became reasonable...
متن کاملPerturbation of Null Spaces with Application to the Eigenvalue Problem and Generalized Inverses
We consider properties of a null space of an analytically perturbed matrix. In particular, we obtain Taylor expansions for the eigenvectors which constitute a basis for the perturbed null space. Furthermore, we apply these results to the calculation of Puiseux expansion of the perturbed eigenvectors in the case of general eigenvalue problem as well as to the calculation of Laurent series expans...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001