Results 31 to 40 of about 1,313 (102)
A closer look at some new identities
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 3, Page 581-586, 1998., 1998 We obtain infinite products related to the concept of visible from the origin point vectors. Among these is in which φ3(k) denotes for fixed k, the number of positive integer solutions of (a, b, k) = 1 where a < b < k, assuming (a, b, k) is the gcd(a, b, k).
Geoffrey B. Campbell
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Visible point vector summations from hypercube and hyperpyramid lattices
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 4, Page 741-748, 1998., 1998 New identities are given, based on ideas related to visible (from the origin) point vectors. Each result was found from summing on vpv lattices dividing space into radial regions from the origin. This is related to recent work by the author in which new partition type infinite products were derived.
Geoffrey B. Campbell
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Differential equations associated with generalized Bell polynomials and their zeros
Open Mathematics, 2016 In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials.
Ryoo Seoung Cheon
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Some new identities of Bernoulli, Euler and Hermite polynomials arising from umbral calculus
, 2013 In this paper, we derive the identities of higher-order Bernoulli, Euler and Frobenius-Euler polynomials from the orthogonality of Hermite polynomials.
Dae San Kim +3 more
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n‐Color partitions with weighted differences equal to minus two
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 759-768, 1997., 1997 In this paper we study those n‐color partitions of Agarwal and Andrews, 1987, in which each pair of parts has weighted difference equal to −2 Results obtained in this paper for these partitions include several combinatorial identities, recurrence relations, generating functions, relationships with the divisor function and computer produced tables.
A. K. Agarwal, R. Balasubrananian
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Discrete Mathematics & Theoretical Computer Science, 2017 Given a set $Y$ of decreasing plane trees and a permutation $\pi$, how many trees in $Y$ have $\pi$ as their postorder? Using combinatorial and geometric constructions, we provide a method for answering this question for certain sets $Y$ and all ...
Colin Defant
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New formulae of products of the Frobenius-Euler polynomials
, 2014 In this paper, we perform a further investigation for the Frobenius-Euler polynomials. Some new formulae of products of the Frobenius-Euler polynomials are established by applying the generating function methods and some summation transform techniques ...
Yuan He, Sherry J Wang
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SOME ALGEBRAIC RELATIONS ON AN INTEGER SEQUENCE WITH FIXED PARAMETER
Acta Universitatis Apulensis, 2019 Let a ≥ 2 be an integer. In this work we set an integer sequence Ua n = Un(a+ 1, a) and deduced some algebraic relations on it. 2010 Mathematics Subject Classification: 05A19, 11B37, 11B39.
Arzu Özkoç Öztürk, A. Tekcan
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Some identities of higher-order Bernoulli, Euler, and Hermite polynomials arising from umbral calculus [PDF]
, 2013 In this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler, and Hermite polynomials arising from umbral calculus to have alternative ways ...
Dae San Kim +3 more
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A generalized formula of Hardy
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 2, Page 369-378, 1994., 1994 We give new formulae applicable to the theory of partitions. Recent work suggests they also relate to quasi‐crystal structure and self‐similarity. Other recent work has given continued fractions for the type of functions herein. Hardy originally gave such formulae as ours in early work on gap power series which led to his and Littlewood′s High Indices ...
Geoffrey B. Campbell
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