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Abstract and Applied Analysis
Volume 2009, Article ID 168672, 18 pages
http://dx.doi.org/10.1155/2009/168672
Review Article

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

Department of Mathematics, Ohio Northern University, Ada, OH 45810, USA

Received 15 May 2009; Accepted 4 August 2009

Academic Editor: Lance Littlejohn

Copyright © 2009 Khristo N. Boyadzhiev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [31 citations]

The following is the list of published articles that have cited the current article.

  • Dmitry V. Kruchinin, Yuriy V. Shablya, Oleg O. Evsutin, and Alexander A. Shelupanov, “Integer properties of a composition of exponential generating functions,” vol. 1863, pp. 300014, . View at Publisher · View at Google Scholar
  • Dmitry V. Kruchinin, and Vladimir V. Kruchinin, “About some properties of polynomials defined by generating functions of form F(t, x)α · G(t, α)x,” vol. 1863, pp. 300015, . View at Publisher · View at Google Scholar
  • Kam Wai C. Chan, Malcolm N. O'Sullivan, and Robert W. Boyd, “Optimization of thermal ghost imaging: high-order correlations vs background subtraction,” Optics Express, vol. 18, no. 6, pp. 5562, 2010. View at Publisher · View at Google Scholar
  • Riccardo Borghi, “Asymptotic and factorial expansions of Euler series truncation errors via exponential polynomials,” Applied Numerical Mathematics, vol. 60, no. 12, pp. 1242–1250, 2010. View at Publisher · View at Google Scholar
  • Ayhan Dil, and Veli Kurt, “Polynomials Related To Harmonic Numbers And Evaluation Of Harmonic Number Series Ii,” Applicable Analysis And Discrete Mathematics, vol. 5, no. 2, pp. 212–229, 2011. View at Publisher · View at Google Scholar
  • Marius Hofert, Martin Mächler, and Alexander J. McNeil, “Likelihood inference for Archimedean copulas in high dimensions under known margins,” Journal of Multivariate Analysis, vol. 110, pp. 133–150, 2012. View at Publisher · View at Google Scholar
  • Enzo Orsingher, and Federico Polito, “Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes,” Journal Of Statistical Physics, vol. 148, no. 2, pp. 233–249, 2012. View at Publisher · View at Google Scholar
  • Nicolas Privault, “Girsanov Identities For Poisson Measures Under Quasi-Nilpotent Transformations,” Annals Of Probability, vol. 40, no. 3, pp. 1009–1040, 2012. View at Publisher · View at Google Scholar
  • Khristo N. Boyadzhiev, and Ayhan Dil, “Series with Hermite polynomials and applications,” Publicationes Mathematicae-Debrecen, vol. 80, no. 3-4, pp. 385–404, 2012. View at Publisher · View at Google Scholar
  • Khristo N. Boyadzhiev, “Close encounters with the stirling numbers of the second kind,” Mathematics Magazine, vol. 85, no. 4, pp. 252–266, 2012. View at Publisher · View at Google Scholar
  • Dmitry V. Kruchinin, and Vladimir V. Kruchinin, “Application of a composition of generating functions for obtaining explicit formulas of polynomials,” Journal of Mathematical Analysis and Applications, vol. 404, no. 1, pp. 161–171, 2013. View at Publisher · View at Google Scholar
  • Marius Hofert, and David Pham, “Densities of nested Archimedean copulas,” Journal of Multivariate Analysis, vol. 118, pp. 37–52, 2013. View at Publisher · View at Google Scholar
  • Toufik Mansour, and Matthias Schork, “The generalized Touchard polynomials revisited,” Applied Mathematics and Computation, vol. 219, no. 19, pp. 9978–9991, 2013. View at Publisher · View at Google Scholar
  • Mohammad Khalid Rafat Khan, “Application of Z-transform on a new polynomial set,” Georgian Mathematical Journal, vol. 20, no. 4, pp. 687–705, 2013. View at Publisher · View at Google Scholar
  • Dimitri Polyakov, “New analytic solutions in string field theory: Towards a collective higher spin vacuum,” Physical Review D, vol. 90, no. 8, 2014. View at Publisher · View at Google Scholar
  • Toufik Mansour, and Matthias Schork, “Bibliography,” Commutation Relations, Normal Ordering, and Stirling Numbers, pp. 419–480, 2015. View at Publisher · View at Google Scholar
  • Toufik Mansour, and Matthias Schorkpp. 1–481, 2015. View at Publisher · View at Google Scholar
  • Levent Kargın, and Roberto B. Corcino, “Generalization of Mellin derivative and its applications,” Integral Transforms and Special Functions, pp. 1–12, 2016. View at Publisher · View at Google Scholar
  • Kh. N. Boyadzhiev, and A. Dil, “Geometric polynomials: properties and applications to series with zeta values,” Analysis Mathematica, vol. 42, no. 3, pp. 203–224, 2016. View at Publisher · View at Google Scholar
  • Nicolas Privault, “Combinatorics of Poisson Stochastic Integrals with Random Integrands,” Bocconi and Springer Series, vol. 7, pp. 37–80, 2016. View at Publisher · View at Google Scholar
  • Khristo N. Boyadzhiev, “Lah numbers, Laguerre polynomials of order negative one, and the nth derivative of exp(1/x),” Acta Universitatis Sapientiae, Mathematica, vol. 8, no. 1, pp. 22–31, 2016. View at Publisher · View at Google Scholar
  • Vasile Pop, and Ovidiu Furduipp. 1–370, 2017. View at Publisher · View at Google Scholar
  • Vasile Pop, Ovidiu Furdui, Vasile Pop, and Ovidiu Furdui, “Functions of matrices. Matrix calculus,” Square Matrices of Order 2, pp. 183–280, 2017. View at Publisher · View at Google Scholar
  • Alwin Kienle, and Andre Liemert, “Computational solutions of the tempered fractional wave-diffusion equation,” Fractional Calculus and Applied Analysis, vol. 20, no. 1, pp. 139–158, 2017. View at Publisher · View at Google Scholar
  • Levent Kargın, “p-Bernoulli and geometric polynomials,” International Journal of Number Theory, pp. 1–20, 2017. View at Publisher · View at Google Scholar
  • Mansour, and Herscovici, “Tsallis p,q-deformed Touchard polynomials and Stirling numbers,” Russian Journal of Mathematical Physics, vol. 24, no. 1, pp. 37–50, 2017. View at Publisher · View at Google Scholar
  • Yu. A. Brychkov, “Some properties of the exponential polynomials,” Integral Transforms and Special Functions, pp. 1–9, 2018. View at Publisher · View at Google Scholar
  • Feng Qi, “On multivariate logarithmic polynomials and their properties,” Indagationes Mathematicae, 2018. View at Publisher · View at Google Scholar
  • Levent Kargin, and Bayram Çekim, “Higher order generalized geometric polynomials,” Turkish Journal of Mathematics, vol. 42, no. 3, pp. 887–903, 2018. View at Publisher · View at Google Scholar
  • Francisco Solis, “Evolution of an Exponential Polynomial Family of Discrete Dynamical Systems,” Mathematical and Computational Applications, vol. 24, no. 1, pp. 13, 2019. View at Publisher · View at Google Scholar
  • Simon R. Blackburn, Cheyne Homberger, and Peter Winkler, “The minimum Manhattan distance and minimum jump of permutations,” Journal of Combinatorial Theory, Series A, vol. 161, pp. 364–386, 2019. View at Publisher · View at Google Scholar