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Abel's Convolution Formulae through Taylor Polynomials

Yıl 2023, , 47 - 51, 30.11.2023
https://doi.org/10.47087/mjm.1314434

Öz

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

Kaynakça

  • N. H. Abel, Beweis eines Ausdrucks, von welchem die Binomial–Formel ein einzelner Fall ist, J. Reine Angew. Math. 1 (1826), 159–160.
  • W. Chu, Inversion techniques and combinatorial identities: A quick introduction to hypergeometric evaluations, Math. Appl. 283 (1994), 31–57.
  • W. Chu, Generating functions and combinatorial identities, Glas. Mat. 33 (1998), 1–12.
  • W. Chu, Elementary Proofs for Convolution Identities of Abel and Hagen–Rothe, Electron. J. Combin. 17 (2010), N24.
  • W. Chu, Finite differences and terminating hypergeometric series, Bull. Irish Math. Soc. 78 (2016), 31–45.
  • W. Chu and L. C. Hsu, Some new applications of Gould-Hsu inversions, J. Combin. Inf. Syst. Sci. 14:1 (1990), 1–4.
  • L. Comtet, Advanced Combinatorics, Dordrecht–Holland, The Netherlands, 1974.
  • 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.
  • H. W. Gould, Some generalizations of Vandermonde’s convolution, Amer. Math. Monthly 63:1 (1956), 84–91.
  • H. W. Gould, Generalization of a theorem of Jensen concerning convolutions, Duke Math. J. 27 (1960), 71–76.
  • H. W. Gould, Combinatorial Identities: a standardized set of tables listing 500 binomial coefficient summations, West Virginia University, Morgantown, 1972.
  • H. W. Gould and L. C. Hsu, Some new inverse series relations, Duke Math. J. 40 (1973), 885–891.
  • R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics (2nd edition), AddisonWesley Publ. Company, Reading, Massachusetts, 1994.
  • J. L. W. V. Jensen, Sur une identite d Abel et sur d’autres formules analogues, Acta Math. 26 (1902), 307–318.
  • S. G. Mohanty, Lattice Path Counting and Applications, Z. W. Birnbaum and E. Lukacs, 1979.
  • T. V. Narayana, Lattice Path Combinatorics with Statistical Applications, University of Toronto Press, Toronto - 1979.
  • J. Riordan, Combinatorial Identities, John Wiley Sons, Inc. New York - 1968.
  • R. Sprugnoli, Riordan arrays and the Abel–Gould identity, Discrete Math. 142 (1995), 213– 233.
  • V. Strehl, Identities of Rothe–Abel–Schl¨afli–Hurwitz–type, Discrete Math. 99:1–3 (1992), 321– 340.
  • P. J. Zucker, Problem 1578, Math. Mag. 72:1 (1999), page 237; Solution: ibid 73:3 (2000), 243–245.
Yıl 2023, , 47 - 51, 30.11.2023
https://doi.org/10.47087/mjm.1314434

Öz

Kaynakça

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

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik (Diğer)
Bölüm Articles
Yazarlar

Wenchang Chu 0000-0002-8425-212X

Erken Görünüm Tarihi 30 Kasım 2023
Yayımlanma Tarihi 30 Kasım 2023
Kabul Tarihi 24 Kasım 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Chu, W. (2023). Abel’s Convolution Formulae through Taylor Polynomials. Maltepe Journal of Mathematics, 5(2), 47-51. https://doi.org/10.47087/mjm.1314434
AMA Chu W. Abel’s Convolution Formulae through Taylor Polynomials. Maltepe Journal of Mathematics. Kasım 2023;5(2):47-51. doi:10.47087/mjm.1314434
Chicago Chu, Wenchang. “Abel’s Convolution Formulae through Taylor Polynomials”. Maltepe Journal of Mathematics 5, sy. 2 (Kasım 2023): 47-51. https://doi.org/10.47087/mjm.1314434.
EndNote Chu W (01 Kasım 2023) Abel’s Convolution Formulae through Taylor Polynomials. Maltepe Journal of Mathematics 5 2 47–51.
IEEE W. Chu, “Abel’s Convolution Formulae through Taylor Polynomials”, Maltepe Journal of Mathematics, c. 5, sy. 2, ss. 47–51, 2023, doi: 10.47087/mjm.1314434.
ISNAD Chu, Wenchang. “Abel’s Convolution Formulae through Taylor Polynomials”. Maltepe Journal of Mathematics 5/2 (Kasım 2023), 47-51. https://doi.org/10.47087/mjm.1314434.
JAMA Chu W. Abel’s Convolution Formulae through Taylor Polynomials. Maltepe Journal of Mathematics. 2023;5:47–51.
MLA Chu, Wenchang. “Abel’s Convolution Formulae through Taylor Polynomials”. Maltepe Journal of Mathematics, c. 5, sy. 2, 2023, ss. 47-51, doi:10.47087/mjm.1314434.
Vancouver Chu W. Abel’s Convolution Formulae through Taylor Polynomials. Maltepe Journal of Mathematics. 2023;5(2):47-51.

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