Results 1 to 10 of about 7,843 (93)
A Unified Generalization of the Catalan, Fuss, and Fuss–Catalan Numbers
Mathematical and Computational Applications, 2019 In the paper, the authors introduce a unified generalization of the Catalan numbers, the Fuss numbers, the Fuss−Catalan numbers, and the Catalan−Qi function, and discover some properties of the unified generalization, including a product ...
Feng Qi, Xiao-Ting Shi, Pietro Cerone
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Some Properties of the Fuss–Catalan Numbers
Mathematics, 2018 In the paper, the authors express the Fuss⁻Catalan numbers as several forms in terms of the Catalan⁻Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the ...
Feng Qi, Pietro Cerone
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Moments of Askey-Wilson polynomials [PDF]
, 2013 New formulas for the nth moment of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux.
Dennis Stanton, Jang Soo, Kim
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Integral Representations of the Catalan Numbers and Their Applications
Mathematics, 2017 In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations ...
Feng Qi, Bai-Ni Guo
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Three Identities of the Catalan-Qi Numbers
Mathematics, 2016 In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternative proofs of two identities of the Catalan numbers. The three identities of the Catalan-Qi numbers generalize three identities of the Catalan numbers.
Mansour Mahmoud, Feng Qi
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Services within a busy period of an M/M/1 queue and Dyck paths [PDF]
, 2005 We analyze the service times of customers in a stable M/M/1 queue in equilibrium depending on their position in a busy period. We give the law of the service of a customer at the beginning, at the end, or in the middle of the busy period. It enables as a
A. Schwartz +13 more
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Baby Universes in String Theory [PDF]
, 2005 We argue that the holographic description of four-dimensional BPS black holes naturally includes multi-center solutions. This suggests that the holographic dual to the gauge theory is not a single AdS_2 times S^2 but a coherent ensemble of them.
A. A. Migdal +11 more
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A Case Study in Meta-AUTOMATION: AUTOMATIC Generation of Congruence AUTOMATA For Combinatorial Sequences [PDF]
, 2013 This article is a sequel to a recent article by Eric Rowland and Reem Yassawi, presenting yet another approach to the fast determination of congruence properties of `famous' combinatorial sequences.
Rowland, Eric, Zeilberger, Doron
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The land–sea coastal border: a quantitative definition by considering the wind and wave conditions in a wave-dominated, micro-tidal environment [PDF]
, 2019 A quantitative definition for the land–sea (coastal) transitional area is proposed here for wave-driven areas, based on the variability and isotropy of met-ocean processes.
García León, Manuel +4 more
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Asymptotic zero distribution of Jacobi-Pi\~neiro and multiple Laguerre polynomials
, 2016 We give the asymptotic distribution of the zeros of Jacobi-Pi\~neiro polynomials and multiple Laguerre polynomials of the first kind. We use the nearest neighbor recurrence relations for these polynomials and a recent result on the ratio asymptotics of ...
Neuschel, Thorsten, Van Assche, Walter
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