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Volumn 50, Issue 11, 2009, Pages

Some applications of the fractional Poisson probability distribution

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EID: 72249122533     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3255535     Document Type: Article
Times cited : (70)

References (23)
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    • (Chapman and Hall, London / CRC, Boca Raton, FL), Chap.
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    • edited by A. Erd́lyi (McGraw-Hill, New York), Chap.
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    • Note
    • The relationship between Bell numbers and the diagonal matrix element of the nth power of the number operator (a+ a) n on the basis of the standard coherent states z〉 at z =1 has been found in Ref.
  • 18
    • 72249105197 scopus 로고    scopus 로고
    • 1730, Note
    • Stirling numbers, introduced by Stirling (Ref.) in 1730, have been studied in the past by many celebrated mathematicians. Among them are Euler, Lagrange, Laplace, and Cauchy. Stirling numbers play an important role in combinatorics, number theory, probability, and statistics. There are two common sets of Stirling numbers, they are the so-called Stirling numbers of the first kind and Stirling numbers of the second kind (for details, see Refs.).
  • 19
    • 0005013402 scopus 로고
    • Stirling numbers of the second kind
    • 9th ed., edited by M. Abramowitz, and I. A. Stegun (Dover, New York), Sec. 24.1.4
    • Stirling Numbers of the Second Kind, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th ed., edited by, M. Abramowitz, and, I. A. Stegun, (Dover, New York, 1972), Sec. 24.1.4, pp. 824-825.
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  • 20
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    • Bernoulli and Euler Polynomials and the Euler-Maclarin Formula
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    • Bernoulli and Euler Polynomials and the Euler-Maclarin Formula, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th ed., edited by, M. Abramowitz, and, I. A. Stegun, (Dover, New York, 1972), Sec. 23.1, p. 804.
    • (1972) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , pp. 804
  • 21
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    • Note
    • μ2-were first obtained by Laskin [see Eqs. (26) and (27) in Ref.]. The second order moment defined by Eq. can be presented as Eq. (27) of Ref. if we take into account the well-known equations for the gamma function (μ), (μ+1) =μ (μ), and (2μ) = 22μ-1 /π (μ) (μ+ 1 2).
  • 22
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    • from MathWorld-A Wolfram Web Resource.
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  • 23
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* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.