منابع مشابه
Some Remarks on Infinite Series
In the present paper we investigate the following problems. Suppose an >O for n_-I and Z a,=-. n=1 N° 1. Does there exist a sequence of natural numbers No =O, Ni l-, such that it decomposes the series monotone decreasingly : In order to state the second problem we define the index nk (c) as the minimum m such that (2) Now the second problem is as follows. are equiconvergent. m kc a j. j=1 N° 2....
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The main purpose of this paper is to present a number of potentially useful integral representations for the familiar Mathieu a-series as well as for its alternating version. These results are derived here from many different considerations and are shown to yield sharp bounding inequalities involving the Mathieu and alternating Mathieu a-series. Relationships of the Mathieu a-series with the Ri...
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Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.
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1 Introduction The aim of this paper is to contribute to the study of the algebra of bounded Dirichlet series. But we must first recall several definitions, notations, and facts. The analytic theory of Dirichlet series is similar to that of power series, but with important differences: whereas a power series has one radius of convergence, a Dirichlet series f (s) = ∞ 1 a n n −s , s = σ + it (1....
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Nonpolynomial basic hypergeometric eigenfunctions of the Askey–Wilson second order difference operator are known to be expressible as very-well-poised 8φ7 series. In this paper we use this fact to derive various basic hypergeometric and theta function identities. We relate most of them to identities from the existing literature on basic hypergeometric series. This leads for example to a new der...
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ژورنال
عنوان ژورنال: ISRN Applied Mathematics
سال: 2014
ISSN: 2090-5572
DOI: 10.1155/2014/985782