The commutation relation xy=qyx+hf(y) and Newton's binomial formula

Toufik Mansour; Matthias Schork

doi:https://doi.org/10.1007/s11139-011-9295-0

The commutation relation xy=qyx+hf(y) and Newton's binomial formula

Toufik Mansour, Matthias Schork

Department of Mathematics

University of Haifa

Research output: Contribution to journal › Article › peer-review

Abstract

Let x and y be two variables satisfying the commutation relation xy=qyx+hf(y), where f(y) is a polynomial. In this paper, using Young diagrams and generating functions techniques, we study the binomial formula (x+y)ⁿ and we present an identity for x^my. The connection to Operator Calculus is discussed and several special cases are treated explicitly.

Original language	American English
Pages (from-to)	405-445
Number of pages	41
Journal	Ramanujan Journal
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/s11139-011-9295-0
State	Published - Aug 2011

Keywords

Operator calculus
Special functions
Young diagrams
q-commuting variables

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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https://doi.org/10.1007/s11139-011-9295-0

Cite this

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title = "The commutation relation xy=qyx+hf(y) and Newton's binomial formula",

abstract = "Let x and y be two variables satisfying the commutation relation xy=qyx+hf(y), where f(y) is a polynomial. In this paper, using Young diagrams and generating functions techniques, we study the binomial formula (x+y)n and we present an identity for xmy. The connection to Operator Calculus is discussed and several special cases are treated explicitly.",

keywords = "Operator calculus, Special functions, Young diagrams, q-commuting variables",

author = "Toufik Mansour and Matthias Schork",

year = "2011",

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AU - Mansour, Toufik

AU - Schork, Matthias

PY - 2011/8

Y1 - 2011/8

N2 - Let x and y be two variables satisfying the commutation relation xy=qyx+hf(y), where f(y) is a polynomial. In this paper, using Young diagrams and generating functions techniques, we study the binomial formula (x+y)n and we present an identity for xmy. The connection to Operator Calculus is discussed and several special cases are treated explicitly.

AB - Let x and y be two variables satisfying the commutation relation xy=qyx+hf(y), where f(y) is a polynomial. In this paper, using Young diagrams and generating functions techniques, we study the binomial formula (x+y)n and we present an identity for xmy. The connection to Operator Calculus is discussed and several special cases are treated explicitly.

KW - Operator calculus

KW - Special functions

KW - Young diagrams

KW - q-commuting variables

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DO - https://doi.org/10.1007/s11139-011-9295-0

M3 - Article

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VL - 25

SP - 405

EP - 445

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 3

ER -

The commutation relation xy=qyx+hf(y) and Newton's binomial formula

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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