Analysis Mathematica

, Volume 25, Issue 1, pp 133–146 | Cite as

Determinants, sums involving binomial coefficients, and moment sequences

  • Zoltán Sasvári
  • Э. Щащвари


In the present paper we investigate some problems connected with the positive definiteness of the sequences\(j \to e^{j^\alpha } (j \in N_0 )\) and\(j \to e^{ - \left| j \right|^\alpha } (j \in Z)\), whereα≥0. For this we need and prove some results about certain determinants and finite sums that might be of independent interest.


Nonnegative Integer Independent Interest Positive Semidefinite Positive Definiteness Binomial Coefficient 
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Определители, суммы, содерзашие биномиаляные коЭффициенты, и последователяности моментов


Иэучаутся полозителяная определенностя некоторых функции и своиства последователяностеи моментов (именно, последователяностеи моментов тригонометрическои и Гамбургера). Согласно классическому реэулятату Герголяца последователяностяf является последователяностяу моментов Гамбургера в том и толяко том случае, когда она полозителяно определена на полугруппеH 0, т.е. когда матрица (f(j+k)) jk n полозителяно полуопределена для всех полозителяныхn.

Иэучаутся специаляное вазные последователяности
$$f_\alpha (j) = \exp (j^\alpha ), g_\alpha (j) = \exp ( - \left| j \right|^\alpha ).$$
Получены некоторые реэулятаты дляf α p иα α p .


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Copyright information

© Akadémiai Kiadó 1999

Authors and Affiliations

  1. 1.Department of MathematicsTechnical University of DresdenDresdenGermany

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