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Exponential Polynomials, Stirling Numbers, and Evaluation of Some Gamma Integrals

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  • Khristo N. Boyadzhiev

Abstract

This article is a short elementary review of the exponential polynomials (also called single‐variable Bell polynomials) from the point of view of analysis. Some new properties are included, and several analysis‐related applications are mentioned. At the end of the paper one application is described in details—certain Fourier integrals involving Γ(a + it) and Γ(a + it)Γ(b − it) are evaluated in terms of Stirling numbers.

Suggested Citation

  • Khristo N. Boyadzhiev, 2009. "Exponential Polynomials, Stirling Numbers, and Evaluation of Some Gamma Integrals," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    • Handle: RePEc:wly:jnlaaa:v:2009:y:2009:i:1:n:168672
    DOI: 10.1155/2009/168672
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    References listed on IDEAS

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    1. J. Sándor & B. Crstici, 2004. "Handbook of Number Theory II," Springer Books, Springer, number 978-1-4020-2547-1, March.
    2. Khristo N. Boyadzhiev, 2005. "A series transformation formula and related polynomials," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-18, January.
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    Cited by:

    1. Hofert, Marius & Pham, David, 2013. "Densities of nested Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 37-52.
    2. Mahid M. Mangontarum, 2023. "Bivariate extension of the r-Dowling polynomials and two forms of generalized Spivey’s formula," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(3), pages 703-712, September.
    3. Freud, Thomas & Rodriguez, Pablo M., 2023. "The Bell–Touchard counting process," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    4. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
    5. Tariq Al-Hawary & Mohamed Illafe & Feras Yousef, 2025. "Certain Constraints for Functions Provided by Touchard Polynomials," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).

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