Multidimensional Catalan and related numbers as Hausdorff moments

• Autorzy: Górska K. , Penson K. A.
• Języki publikacji: EN

Abstrakty

EN

We study integral representation of the so-called d-dimensional Catalan numbers C_d(n), defined by [Π^d−1_p=0 p!=(n + p)!] (dn)!, d = 2, 3, …, n = 0, 1, …We prove that the C_d(n)’s are the nth Hausdorff power moments of positive functions W_d(x) defined on x ∈ [0, d^d]. We construct exact and explicit forms of W_d(x) and demonstrate that they can be expressed as combinations of d−1 hypergeometric functions of type _d−1F_d−2 of argument x/d^d. These solutions are unique. We analyze tchem analytically and graphically. A combinatorially relevant, specific extension of C_d(n) for d even in the form D^d(n) = [wzór] is analyzed along the same lines.

Słowa kluczowe

EN

d-dimensional Catalan numbers; Hausdorff moment problem

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2013
• Tom: Vol. 33, Fasc. 2
• Strony: 265--274
• Opis fizyczny: Bibliogr. 19 poz., tab., wykr.

Twórcy

autor

Górska K.

• H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, ul. Eljasza-Radzikowskiego 152, 31-342 Kraków, Poland

autor

Penson K. A.

• Laboratoire de Physique Théorique, de la Matière Condensée (LPTMC), Université Pierre et Marie Curie, CNRS UMR 7600, Tour 13 – 5ième ét., Boîte Courrier 121, 4 place Jussieu, F 75252 Paris Cedex 05, France

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).