Abstract
In this article we prove an algebraic identity which significantly generalizes the formula for sum of powers of consecutive integers involving Stirling numbers of the second kind. Also we have obtained a generalization of Newton-Girard power sum identity.
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References
Bapat, R.B., Roy, S.: Cayley-Hamilton theorem for mixed discriminants. J. Comb. Math. Comb. Comput 101, 223–231 (2017)
Boyadzhiev, K.N.: Power sum identities with generalized Stirling numbers. Fibonacci Q. 47(4), 326–330 (2009)
Mukherjee, S.K., Bera, S.: Combinatorial proofs of the Newton-Girard and Chapman-Costas-Santos identities. Discrete Math. 342, 1577–1580 (2019)
Zeilberger, D.: A combinatorial proof of newton’s identity. Discrete Math. 49, 319 (1984)
Acknowledgements
The first author was supported by Department of Science and Technology grant EMR/2016/006624 and partly supported by UGC Centre for Advanced Studies. Also the first author was supported by NBHM Post Doctoral Fellowship grant 0204/52/2019/RD-II/339. The second author was supported by NBHM Post Doctoral Fellowship grant 0204/3/2020/RD-II/2470. The authors would like to thank the anonymous referees for their meticulous reading of the manuscript and valuable suggestions that significantly improved the exposition of this paper.
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Bera, S., Mukherjee, S.K. Generalized Power Sum and Newton-Girard Identities. Graphs and Combinatorics 36, 1957–1964 (2020). https://doi.org/10.1007/s00373-020-02223-3
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DOI: https://doi.org/10.1007/s00373-020-02223-3