Journals / Maltepe Journal of Mathematics / 2023 / Volume: 5 Issue: 2

Abel's Convolution Formulae through Taylor Polynomials

Wenchang Chu(university of salento)0000-0002-8425-212X
Pages
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Publication Date
2023-11-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

By making use of the Taylor polynomials, new proofs are presented for three binomial identities including Abel’s convolution formula.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:By making use of the Taylor polynomials, new proofs are presented for three binomial identities including Abel’s convolution formula.
📊
Key Findings & Data:By making use of the Taylor polynomials, new proofs are presented for three binomial identities including Abel’s convolution formula.
💡
Conclusion & Impact:By making use of the Taylor polynomials, new proofs are presented for three binomial identities including Abel’s convolution formula.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:The binomial theorem · Taylor polynomial · Abel’s convolution formulae

Abstract

By making use of the Taylor polynomials, new proofs are presented for three binomial identities including Abel’s convolution formula.

🔖

Cite This Article

Chu, W. (2023). Abel's Convolution Formulae through Taylor Polynomials. Maltepe Journal of Mathematics, Volume: 5 Issue: 2. https://doi.org/10.47087/mjm.1314434

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References (20)

  1. N. H. Abel, Beweis eines Ausdrucks, von welchem die Binomial–Formel ein einzelner Fall ist, J. Reine Angew. Math. 1 (1826), 159–160.
  2. W. Chu, Inversion techniques and combinatorial identities: A quick introduction to hypergeometric evaluations, Math. Appl. 283 (1994), 31–57.
  3. W. Chu, Generating functions and combinatorial identities, Glas. Mat. 33 (1998), 1–12.
  4. W. Chu, Elementary Proofs for Convolution Identities of Abel and Hagen–Rothe, Electron. J. Combin. 17 (2010), N24.
  5. W. Chu, Finite differences and terminating hypergeometric series, Bull. Irish Math. Soc. 78 (2016), 31–45.
  6. W. Chu and L. C. Hsu, Some new applications of Gould-Hsu inversions, J. Combin. Inf. Syst. Sci. 14:1 (1990), 1–4.
  7. L. Comtet, Advanced Combinatorics, Dordrecht–Holland, The Netherlands, 1974.
  8. G. P. Egorychev, Integral Representation and the Computation of Combinatorial Sums, Translated from the Russian by H. H. McFadden: Translations of Mathematical Monographs 59; American Mathematical Society, Providence, RI, 1984. 286pp.
  9. H. W. Gould, Some generalizations of Vandermonde’s convolution, Amer. Math. Monthly 63:1 (1956), 84–91.
  10. H. W. Gould, Generalization of a theorem of Jensen concerning convolutions, Duke Math. J. 27 (1960), 71–76.
  11. H. W. Gould, Combinatorial Identities: a standardized set of tables listing 500 binomial coefficient summations, West Virginia University, Morgantown, 1972.
  12. H. W. Gould and L. C. Hsu, Some new inverse series relations, Duke Math. J. 40 (1973), 885–891.
  13. R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics (2nd edition), AddisonWesley Publ. Company, Reading, Massachusetts, 1994.
  14. J. L. W. V. Jensen, Sur une identite d Abel et sur d’autres formules analogues, Acta Math. 26 (1902), 307–318.
  15. S. G. Mohanty, Lattice Path Counting and Applications, Z. W. Birnbaum and E. Lukacs, 1979.
  16. T. V. Narayana, Lattice Path Combinatorics with Statistical Applications, University of Toronto Press, Toronto - 1979.
  17. J. Riordan, Combinatorial Identities, John Wiley Sons, Inc. New York - 1968.
  18. R. Sprugnoli, Riordan arrays and the Abel–Gould identity, Discrete Math. 142 (1995), 213– 233.
  19. V. Strehl, Identities of Rothe–Abel–Schl¨afli–Hurwitz–type, Discrete Math. 99:1–3 (1992), 321– 340.
  20. P. J. Zucker, Problem 1578, Math. Mag. 72:1 (1999), page 237; Solution: ibid 73:3 (2000), 243–245.