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q-Engel Series Expansions and Slaters Identities
George E Andrews, Arnold Knopfmacher, Peter Paule, Helmut Prodinger
Abstract
We describe the q-Engel series expansion for Laurent series discovered by
John Knopfmacher and use this algorithm to shed new light on partition identities
related to two entries from Slater's list. In our study Al-Salam/Ismail and
Santos polynomials play a crucial role.
Mathematics Subject Classification (1991): Primary: 11; Secondary:
11.
Keywords: expansions, q-Engel series, Slaters identities, Engel series,
q-series, Al-Salam polynomials, Ismail polynomials, identities, Santos polynomials,
number theory, John Knopfmacher, partition, study, polynomials
Quaestiones Mathematicae 24(3) 2001, 403-416
John Knopfmacher and use this algorithm to shed new light on partition identities
related to two entries from Slater's list. In our study Al-Salam/Ismail and
Santos polynomials play a crucial role.
Mathematics Subject Classification (1991): Primary: 11; Secondary:
11.
Keywords: expansions, q-Engel series, Slaters identities, Engel series,
q-series, Al-Salam polynomials, Ismail polynomials, identities, Santos polynomials,
number theory, John Knopfmacher, partition, study, polynomials
Quaestiones Mathematicae 24(3) 2001, 403-416
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Quaestiones Mathematicae. ISSN: 1607-3606