Riordan Arrays and Generalized Lagrange Series
Matematičeskie zametki, Tome 100 (2016) no. 4, pp. 510-518.

Voir la notice de l'article provenant de la source Math-Net.Ru

The theory of Riordan arrays studies the properties of formal power series and their sequences. The notion of generalized Lagrange series proposed in the present paper is intended to fill the gap in the methodology of this theory. Generalized Lagrange series appear in it implicitly, as various equalities. No special notation is provided for these series, although particular cases of these series are generalized binomial and generalized exponential series. We give the definition of generalized Lagrange series and study their relationship with ordinary Riordan arrays and, separately, with Riordan exponential arrays.
Keywords: Riordan array, Riordan group, generalized binomial series, Lagrange series.
@article{MZM_2016_100_4_a3,
     author = {E. V. Burlachenko},
     title = {Riordan {Arrays} and {Generalized} {Lagrange} {Series}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {510--518},
     publisher = {mathdoc},
     volume = {100},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a3/}
}
TY  - JOUR
AU  - E. V. Burlachenko
TI  - Riordan Arrays and Generalized Lagrange Series
JO  - Matematičeskie zametki
PY  - 2016
SP  - 510
EP  - 518
VL  - 100
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a3/
LA  - ru
ID  - MZM_2016_100_4_a3
ER  - 
%0 Journal Article
%A E. V. Burlachenko
%T Riordan Arrays and Generalized Lagrange Series
%J Matematičeskie zametki
%D 2016
%P 510-518
%V 100
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a3/
%G ru
%F MZM_2016_100_4_a3
E. V. Burlachenko. Riordan Arrays and Generalized Lagrange Series. Matematičeskie zametki, Tome 100 (2016) no. 4, pp. 510-518. http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a3/

[1] L. Shapiro, S. Getu, W. Woan, L. Woodson, “The Riordan group”, Discrete Appl. Math., 34 (1991), 229–339 | DOI | MR

[2] R. Sprugnoli, “Riordan arrays and combinatorial sums”, Discrete Math., 132 (1994), 267–290 | DOI | MR | Zbl

[3] N. Cameron, A. Nkwanta, “On some (pseudo) involutions in the Riordan group”, J. Ineger. Seq., 8 (2005), 1–16 | MR

[4] G. Cheon, H. Kim, L. Shapiro, “Riordan group involutions”, Linear Algebra Appl., 428 (2008), 941–952 | DOI | MR | Zbl

[5] W. Wang, T. Wang, “Generalized Riordan arrays”, Discrete Math., 308 (2008), 6466–6500 | DOI | MR | Zbl

[6] S. M. Roman, G.-C. Rota, “The umbral calculus”, Adv. Math., 27 (1978), 95–188 | DOI | MR | Zbl

[7] S. M. Roman, The Umbral Calculus, Academic Press, New York, 1984 | MR | Zbl

[8] A. V. Ustinov, “Polinomy Korobova i tenevoi analiz”, Chebyshevskii sb., 2003, no. 4, 1–12

[9] R. Grekhem, D. Knut, O. Patashnik, Konkretnaya matematika, Mir, M., 1998

[10] R. Sprugnoli, “Riordan arrays and Abel-Gould identity”, Discrete Math., 142:1-3 (1995), 213–233 | DOI | MR

[11] E. Brietzke, “An identity of Andrews and a new method for the Riordan array proof of combinatorial identities”, Discrete Math., 308 (2008), 4246–4262 | DOI | MR | Zbl

[12] V. E. Hoggatt Jr., P. S. Bruckman, “H-convolution transform”, Fibonacci Quart., 13:4 (1975), 357–368 | MR | Zbl