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Irrationality of Infinite Series
Mediterranean Journal of Mathematics, 2019The paper deals with linear independence of infinite series over a given algebraic number field. The main result states the following. Let $\mathbb{K}$ be an algebraic number field and let $P_j(X),Q_j(X)\in\mathbb{K}[X]$, $j=1,\dots,R$, be polynomials with $\deg P_j1.
Hančl, Jaroslav, Luca, Florian
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Infinite sequences and infinite series
1977It is customary to use expressions such as $${u_1} + {u_2} + \cdots + {u_n} + \cdots ,\;and\;\sum\limits_{n = 1}^\infty {{u_n}}$$ (9.1) to represent infinite series. The u i are called the terms of the series, and the quantities $${s_n} = {u_1} + {u_2} + \cdots + {u_n},\quad n = 1,2, \ldots ,$$ are called the partial sums of the series.
Murray H. Protter, Charles B. Morrey
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On infinite series of infinite isols
The Journal of Symbolic Logic, 1988We are interested in regressive isols, recursive functions, and the extensions of recursive functions to the isols. One of the nicest concepts that has been applied to the study of these notions is of an infinite series of isols . J. C. E.
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Software: Practice and Experience, 1980
AbstractThe creation, manipulation and evaluation of univariate infinite power series is discussed. Unlike truncated power series, which store the first n terms of an expansion, infinite power series create a procedure for calculating a general term, and are thus a formal representation of the entire expansion.
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AbstractThe creation, manipulation and evaluation of univariate infinite power series is discussed. Unlike truncated power series, which store the first n terms of an expansion, infinite power series create a procedure for calculating a general term, and are thus a formal representation of the entire expansion.
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1992
Abstract Infinite series were in the eighteenth century and are still today considered an essential part of the calculus. Indeed, Newton considered series inseparable from his method of £1.uxions because the only way he could handle even slightly complicated algebraic functions and the transcendental functions was to expand them into ...
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Abstract Infinite series were in the eighteenth century and are still today considered an essential part of the calculus. Indeed, Newton considered series inseparable from his method of £1.uxions because the only way he could handle even slightly complicated algebraic functions and the transcendental functions was to expand them into ...
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SERIES AND INFINITE PRODUCTS OF INFINITE MATRICES
The Quarterly Journal of Mathematics, 1960openaire +2 more sources
Exploring students’ consistency in their notions: the case of comparing infinite series
International Journal of Mathematical Education in Science and Technology, 2021Ali Barahmand
exaly