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Convolutions for Stirling numbers, Lah numbers, and binomial coefficients
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A number of identities are proved, mostly in the form of convolutions, involving Stirling numbers of both kinds, Lah numbers, and binomial coefficients. Certain “convolution polynomials” are discussed also. The proofs are based on several series transformation formulas.
Abstract
A number of identities are proved, mostly in the form of convolutions, involving Stirling numbers of both kinds, Lah numbers, and binomial coefficients. Certain “convolution polynomials” are discussed also. The proofs are based on several series transformation formulas.
참고문헌 (15)
- Victor Adamchik, "On Stirling numbers and Euler sums", J. Comput. Applied Math, 79, pp.119~130 (1997)
- Takashi Agoh, "Convolution identities for Stirling numbers of the first kind", Integers, 10, pp.101~109 (2010)
- Paul Barry, "Some Observations on the Lah and Laguerre Transforms of Integer Sequences", J. Integer Seq., 10, pp.07.4.6~ (2007)
- Khristo N. Boyadzhiev, "Close encounters with the Stirling numbers of the second kind", Math. Mag., 85(4), pp.252~266 (2012)
- Khristo N. Boyadzhiev, "Lah numbers, Laguerre polynomials of order negative one, and the n-th derivative of exp(1", x), 2016, pp.8(1), 22~31
- Khristo N. Boyadzhiev, "New identities withvStirling, hyperharmonic, and derangement numbers, Bernoulli and Euler Polynomials, powers, and factorials", J. Comb. Number Theory, 11(1), pp.43~58 (2019)
- Khristo N. Boyadzhiev, "Notes on the Binomial Transform" (2018), World Scientific
- Andei Z. Broder, "The r-Stirling numbers", Discrete Math., 49, pp.241~259 (1984)
- Charalambos A, "Charalambides, Enumerative Combinatorics", pp.2002, Chapman and Hall
- Junesang Choi, "Certain identities involving Stirling numbers of the first kind", Far East J. Math. Sci. (FJMS), 103(2), pp.523~539 (2018)
- Louis Comtet, "Advanced Combinatorics" (1974), Reidel
- Henry W. Gould, "Series transformations for finding recurrences for sequences", Fibonacci Quart, 28(2), pp.166~171 (1990)
- Ronald. L. Graham, "Concrete Mathematics" (1989), Addison-Wesley
- Alfred Schreiber, "Note on some power sum identities involving Stirling numbers", personal communication
- Pavel G. Todorov, "Taylor expansions of analytic functions related to (1+z)x-1", J. Math. Anal. Appl, 132, pp.264~280 (1988)
관련 논문AI추천
Higher-order convolution identities for Cauchy numbers of the second kindT KOMATSU장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제3호Lah-Bell numbers and polynomials김대산, 김태균장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제4호CENTRAL LAH NUMBERS AND CENTRAL LAH-BELL NUMBERS김혜경장전수학회 · Advanced Studies in Contemporary Mathematics2022 · 제32권 제1호A q-ANALOGUE OF THE GENERALIZED FACTORIAL NUMBERS송석준, 전영배, 천기상, LeRoy B. Beasley대한수학회 · 대한수학회지2010 · 제47권 제3호λ-analogue of stirling numbers of the first kind김태균장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제3호Some identities of symmetry for stirling polynomials김태균, 서종진장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제2호
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