Double Series and Sums
نویسندگان
چکیده
منابع مشابه
On Evaluations of Infinite Double Sums and Tornheim’s Double Series
We consider generalizations of a sum, which was recently analyzed by Pemantle and Schneider using the computer software Sigma, and later also by Panholzer and Prodinger. Our generalizations include Tornheim’s double series as a special case. We also consider alternating analogs of Tornheim’s series. For Tornheim’s double series and its alternating counterparts we provide short proofs for evalua...
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Sylvester double sums versus subresultants given two polynomials A and B first notion symmetric expression of the roots of two polynomials second notion defined through the coefficients polynomials main result of the lecture these two notions are very closely related (idea due to Sylvester [S]) see details and complete proofs in [RS]. 1 Definitions and main result. A and B two finite families o...
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In 1988, Andrews, Dyson and Hickerson initiated the study of q-hypergeometric series whose coefficients are dictated by the arithmetic in real quadratic fields. In this paper, we provide a dozen q-hypergeometric double sums which are generating functions for the number of ideals of a given norm in rings of integers of real quadratic fields and prove some related identities.
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This research considers two traditional important questions, which are interesting, at least to most mathematicians. The first question arises in the theory of double sequences of complex numbers, which concerns the relationship, if any, between the following three limits of a double sequence s : N×N −→ C: 1. limn,m→∞ s(n, m), 2. limn→∞(limm→∞ s(n, m)), 3. limm→∞(limn→∞ s(n, m)). In particular,...
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On page 335 in his lost notebook, Ramanujan records without proof an identity involving a finite trigonometric sum and a doubly infinite series of ordinary Bessel functions. We provide the first published proof of this result. The identity yields as corollaries representations of weighted divisor sums, in particular, the summatory function for r2(n), the number of representations of the positiv...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2014
ISSN: 1898-9934
DOI: 10.2478/forma-2014-0006