Application of Fa´a Di Bruno’s Formula in the Construction of Combinatorial Identities

Tian-Xiao He

Application of Fa´a Di Bruno’s Formula in the Construction of Combinatorial Identities

Illinois Wesleyan University

Research output: Journal Article › Article › peer-review

Abstract

Chou, Hsu, and Shiue in [3] use Fa`a di Bruno’s formula give a class of composite series expansions. In this paper, we apply those expansions to construct a class of identities for Catalan numbers, large Schroder numbers, small Schroder numbers, parametric Catalan numbers, Stirling numbers, binomial numbers, some other recursive

number sequences, and recursive polynomial sequences.

Original language	American English
Journal	Journal of Combinatorics and Number Theory
Volume	7
State	Published - 2015

Keywords

Catalan numbers
Fa´a di Bruno’s Formula
Stirling numbers
binomial numbers
generalized Gegenbauer-Humbert polynomials
large Schr¨oder numbers
recursive number sequences
small Schr¨oder numbers

Disciplines

Mathematics

Access to Document

129_FaadiBrunoFormula.pdfFinal published version, 243 KBLicense: Unspecified

Cite this

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title = "Application of Fa´a Di Bruno{\textquoteright}s Formula in the Construction of Combinatorial Identities",

abstract = " Chou, Hsu, and Shiue in [3] use Fa`a di Bruno{\textquoteright}s formula give a class of composite series expansions. In this paper, we apply those expansions to construct a class of identities for Catalan numbers, large Schroder numbers, small Schroder numbers, parametric Catalan numbers, Stirling numbers, binomial numbers, some other recursive number sequences, and recursive polynomial sequences.",

keywords = "Catalan numbers, Fa´a di Bruno{\textquoteright}s Formula, Stirling numbers, binomial numbers, generalized Gegenbauer-Humbert polynomials, large Schr¨oder numbers, recursive number sequences, small Schr¨oder numbers",

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journal = "Journal of Combinatorics and Number Theory",

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T1 - Application of Fa´a Di Bruno’s Formula in the Construction of Combinatorial Identities

AU - He, Tian-Xiao

PY - 2015

Y1 - 2015

N2 - Chou, Hsu, and Shiue in [3] use Fa`a di Bruno’s formula give a class of composite series expansions. In this paper, we apply those expansions to construct a class of identities for Catalan numbers, large Schroder numbers, small Schroder numbers, parametric Catalan numbers, Stirling numbers, binomial numbers, some other recursive number sequences, and recursive polynomial sequences.

AB - Chou, Hsu, and Shiue in [3] use Fa`a di Bruno’s formula give a class of composite series expansions. In this paper, we apply those expansions to construct a class of identities for Catalan numbers, large Schroder numbers, small Schroder numbers, parametric Catalan numbers, Stirling numbers, binomial numbers, some other recursive number sequences, and recursive polynomial sequences.

KW - Catalan numbers

KW - Fa´a di Bruno’s Formula

KW - Stirling numbers

KW - binomial numbers

KW - generalized Gegenbauer-Humbert polynomials

KW - large Schr¨oder numbers

KW - recursive number sequences

KW - small Schr¨oder numbers

M3 - Article

VL - 7

JO - Journal of Combinatorics and Number Theory

JF - Journal of Combinatorics and Number Theory

ER -