Exponential polynomials, Stirling numbers, and evaluation of some gamma integrals

DOI10.1155/2009/168672zbMath1237.11011arXiv0909.0979OpenAlexW3102191393WikidataQ21342785 ScholiaQ21342785MaRDI QIDQ1035051

Khristo N. Boyadzhiev

Publication date: 10 November 2009

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.0979

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Gamma, beta and polygamma functions (33B15)

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Cites Work

• Mellin transform analysis and integration by parts for Hadamard-type fractional integrals
• Factorial functions and Stirling numbers of fractional orders
• Single variable Bell polynomials
• Fractional calculus in the Mellin setting and Hadamard-type fractional integrals
• Compositions of Hadamard-type fractional integration operators and the semigroup property
• Exponential polynomials
• A uniform asymptotic expansion of the single variable Bell polynomials
• Bell numbers, their relatives, and algebraic differential equations
• A series transformation formula and related polynomials
• Some Probabilistic Aspects of Set Partitions
• Two Notes on Notation
• Nombres Exponentiels Et Nombres De Bernoulli
• On the Taylor Coefficients of the Hurwitz Zeta Function
• A linear binomial recurrence and the Bell numbers and polynomials
• On Stirling Functions of the Second Kind
• Euler's formula nth Differences of Powers
• Exponential Numbers
• Stirling Behavior is Asymptotically Normal
• A Function Related to the Series for
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