A general size-biased distribution

• Autorzy: Patkowski Alexander E.

Identyfikatory

DOI

10.1515/jaa-2023-0003

• Języki publikacji: EN

Abstrakty

EN

We generalize a size-biased distribution related to the Riemann xi-function using the work of Ferrar. Some analysis and properties of this more general distribution are offered as well.

Słowa kluczowe

EN

size-biased distribution; Riemann xi-function; probability

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2023
• Tom: Vol. 29, nr 2
• Strony: 347--351
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Patkowski Alexander E.

• 1390 Bumps River Rd., Centerville, MA 02632, USA

• https://orcid.org/0000-0002-0455-3089

Bibliografia

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• [4] H. M. Edwards, Riemann’s Zeta Function, Pure Appl. Math. 58, Academic Press, New York, 1974.
• [5] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms. Vol. I, McGraw-Hill, New York, 1954.
• [6] W. L. Ferrar, Some Solutions of the Equation F(t) = F(t-1), J. Lond. Math. Soc. 11 (1936), no. 2, 99-103.
• [7] R. E. Gaunt, Inequalities for modified Bessel functions and their integrals, J. Math. Anal. Appl. 420 (2014), no. 1, 373-386.
• [8] F. W. J. Olver, Asymptotics and Special Functions, Comput. Sci. Appl. Math., Academic Press, New York, 1974.
• [9] R. B. Paris and D. Kaminski, Asymptotics and Mellin-Barnes Integrals, Encyclopedia Math. Appl. 85, Cambridge University, Cambridge, 2001.
• [10] L. Smith and P. Diaconis, Honest Bernoulli excursions, J. Appl. Probab. 25 (1988), no. 3, 464-477.
• [11] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed., Oxford University, New York, 1986.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).