Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers
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Publication:508638
DOI10.1515/ausm-2016-0019zbMath1360.11052OpenAlexW2584934510MaRDI QIDQ508638
Fang-Fang Liu, Xiao-Ting Shi, Feng Qi
Publication date: 7 February 2017
Published in: Acta Universitatis Sapientiae. Mathematica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/ausm-2016-0019
Bell and Stirling numbers (11B73) Binomial coefficients; factorials; (q)-identities (11B65) Special sequences and polynomials (11B83)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Several closed expressions for the Euler numbers
- Explicit expressions for a family of the Bell polynomials and applications
- Complete monotonicity of a difference between the exponential and trigamma functions and properties related to a modified Bessel function
- An integral representation, complete monotonicity, and inequalities of Cauchy numbers of the second kind
- A completely monotonic function involving the tri-gamma function and with degree one
- An explicit formula for the Bell numbers in terms of the Lah and Stirling numbers
- On the degree of the weighted geometric mean as a complete Bernstein function
- Explicit formulas for special values of the Bell polynomials of the second kind and for the Euler numbers and polynomials
- Alternative proofs of a formula for Bernoulli numbers in terms of Stirling numbers
- Some identities and an explicit formula for Bernoulli and Stirling numbers
- Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind
- An integral representation for the weighted geometric mean and its applications
- Integral representations and properties of Stirling numbers of the first kind
- Lévy-Khintchine representations of the weighted geometric mean and the logarithmic mean
- Some identities involving exponential functions and Stirling numbers and applications
- Diagonal recurrence relations, inequalities, and monotonicity related to the Stirling numbers of the second kind
- COMPLETE MONOTONICITY OF A DIFFERENCE BETWEEN THE EXPONENTIAL AND TRIGAMMA FUNCTIONS
- Six proofs for an identity of the Lah numbers
- Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions
- Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind
- On complete monotonicity of some functions related to means
- Lévy-Khintchine representation of the geometric mean of many positive numbers and applications
- A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE RATIO OF GAMMA FUNCTIONS
- Limit formulas for ratios between derivatives of the gamma and digamma functions at their singularities
- AN INTEGRAL REPRESENTATION, SOME INEQUALITIES, AND COMPLETE MONOTONICITY OF THE BERNOULLI NUMBERS OF THE SECOND KIND
- A new formula for the Bernoulli numbers of the second kind in terms of the Stirling numbers of the first kind
- Complete monotonicity of the logarithmic mean
- Diagonal recurrence relations for the Stirling numbers of the first kind
- Bernstein functions. Theory and applications
