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

Toufik Mansour, Matthias Schork

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)405-445
Number of pages41
JournalRamanujan Journal
Issue number3
StatePublished - Aug 2011


  • Operator calculus
  • Special functions
  • Young diagrams
  • q-commuting variables

ASJC Scopus subject areas

  • Algebra and Number Theory


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