Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind

By Feng Qi (祁锋). 2013

85 citations recorded by the source corpus.

In the paper, by establishing a new and explicit formula for computing the $n$-th derivative of the reciprocal of the logarithmic function, the author presents new and explicit formulas for calculating Bernoulli numbers of the second kind and Stirling numbers of the first kind. As consequences of these formulas, a recursion for Stirling numbers of the first kind and a new representation of the reciprocal of the factorial $n!$ are derived. Finally, the author finds several identities and integral representations relating to Stirling numbers of the first kind.

Subfields: Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/8690a7677b03778fc6f9d747738bde84db6e3b92

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In Algebra and Number Theory

1. Dongkyu Lim
2. Bai-Ni Guo (郭白妮)
3. Yong-hong Yao
4. Da-Wei Niu
5. Feng Qi (祁锋)
6. Robin J. Chapman
7. Hari M. Srivastava

In Applied Mathematics

1. Bai-Ni Guo (郭白妮)
2. Feng Qi (祁锋)
3. Dongkyu Lim
4. Da-Wei Niu
5. Robin J. Chapman
6. Yong-hong Yao
7. Hari M. Srivastava
8. Chao Chen

In Discrete Mathematics and Combinatorics

1. Dongkyu Lim
2. Bai-Ni Guo (郭白妮)
3. Yong-hong Yao
4. Da-Wei Niu
5. Robin J. Chapman

Citations in the corpus

• An Explicit Formula for the Bell Numbers in Terms of the Lah and Stirling Numbers (2014, background): “Taking f(u) = e and h(x) = e in (5) and making use of (2) gives d e −x dxn = n ∑”
• Two closed forms for the Bernoulli polynomials (2015, background): “There are also some other formulas and inequalities for the Bernoulli numbers and polynomials in [10,11,15,16,24,26,27,29,33] and references cited therein.”
• Special values of the Bell polynomials of the second kind for some sequences and functions (2020, background): “4), please refer to [29, 38, 39, 41, 42, 44, 46, 73, 80, 91, 95, 96] and closely related references therein.”
• Explicit formulas and identities for the Bell polynomials and a sequence of polynomials applied to differential equations (2019, methodology): “The formulas in (5) have applied in [1, 8, 9, 11, 13, 14, 16, 17, 19, 22, 23].”