THE GENERALIZED q-OPERATOR [.sub.r][[PHI].sub.s] AND ITS APPLICATIONS IN q-IDENTITIES

THE GENERALIZED q-OPERATOR [.sub.r][[PHI].sub.s] AND ITS APPLICATIONS IN q-IDENTITIES

Based on the basic hypergeometric series [.sub.r][[phi].sub.s], we construct a new generalized q-operator [.sub.r][[PHI].sub.s] [Please download the PDF to view the mathematical expression] and obtain some of its identities. Using these identities, we generalize several well-known q-identities, such...

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Veröffentlicht in:TWMS journal of applied and engineering mathematics 2023-07, Vol.13 (3), p.1137
Hauptverfasser: Saad, Husam L, Khalaf, Sadeq M
Format: Artikel
Sprache:eng
Schlagworte:
Difference equations
Operator theory
Series
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Zusammenfassung:Based on the basic hypergeometric series [.sub.r][[phi].sub.s], we construct a new generalized q-operator [.sub.r][[PHI].sub.s] [Please download the PDF to view the mathematical expression] and obtain some of its identities. Using these identities, we generalize several well-known q-identities, such as the q-Gauss sum, the q-Chu-Vandermonde sum, and the q-Pffaf-Saalschutz sum. Keywords: The q-operator, q-Gauss sum, q-Chu-Vandermonde sum, q-Pffaf-Saalschutz sum. AMS Subject Classification: 05A30, 33D45.
ISSN:2146-1147