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Open Access
2018
70 sitasi
On the q-Partial Differential Equations and q-Series
Zhi-Guo Liu
Abstrak
Using the theory of functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of q-partial differential equations, then, it can be expanded in terms of the product of the Rogers-Szegý o poly- nomials. This expansion theorem allows us to develop a general method for proving q-identities. A general q-transformation formula is derived, which implies Watson's q-analog of Whipple's theorem as a special case. A multilinear generating function for the Rogers-Szegý o polynomials is given. The theory of q-exponential operator is revisited.
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Zhi-Guo Liu
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- Tahun Terbit
- 2018
- Bahasa
- en
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- Semantic Scholar
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- Open Access ✓