Applications of the generalized homogeneous q-shift operator in q-polynomials
Künye
Adnan Abdul-Ghani, S. & Saad, H. L. (2024). Applications of the generalized homogeneous q-shift operator in q-polynomials. TWMS Journal Of Applied And Engineering Mathematics, 14(2), 473-494.Özet
In this paper, we construct the generalized homogeneous q-shift operatör rΦs ( a1, · · · , ar b1, · · · , bs ; q, cDxy). Then, we apply this operator to derive some q-identities such as: the generating function and its extension, Rogers formula and its extension, Mehler’s formula and its extension, Srivastava-Agarwal type bilinear generating functions for the polynomials φ(a,b)n (x, y, c|q). Also, we obtain a transformation formula involving generating functions for φ(a,b)n (x, y, c|q). We provide some special values for φ(a,b)n (x, y, c|q) in order to establish identities for the polynomials φ(a)n (x) and φ(a,b)n (x, y|q).
Kaynak
TWMS Journal Of Applied And Engineering MathematicsCilt
14Sayı
2Bağlantı
https://hdl.handle.net/11729/5944https://jaem.isikun.edu.tr/web/index.php/current/124-vol14no2/1190
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