Euler’s “exemplum memorabile inductionis Fallacis” and q-trinomial coefficients

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

The trinomial coefficients are defined centrally by (Equation presented). Euler observed that for −1 ≤ m ≤ 7, (Equation presented), where Fm is the mth Fibonacci number. The assertion is false for m > 7. We prove general identities—one of which reduces to Euler’s assertion for m ≤ 7. Our main object is to analyze q-analogs extending Euler’s observation. Among other things we are led to finite versions of dissections of the Rogers-Ramanujan identities into even and odd parts.

Original languageEnglish (US)
Pages (from-to)653-669
Number of pages17
JournalJournal of the American Mathematical Society
Volume3
Issue number3
DOIs
StatePublished - Jan 1 1990

Fingerprint

Dissection
Assertion
Rogers-Ramanujan Identities
Lame number
Q-analogue
Coefficient
Thing
Euler
Odd
Observation
False
Object

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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Euler’s “exemplum memorabile inductionis Fallacis” and q-trinomial coefficients. / Andrews, George E.

In: Journal of the American Mathematical Society, Vol. 3, No. 3, 01.01.1990, p. 653-669.

Research output: Contribution to journalArticle

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