q-Difference equation and q-polynomials

• We establish one general q-exponential operator.
• We give one general q-difference equation.
• Relationship between q-exponential operator and q-difference equation are given.
• Using q-difference equation to set up a q-polynomials Hn.
• Some generating functions for Hn are obtained.

In this paper, we establish one general q-exponential operator identity by solving one simple q-difference equation. Using this q  -difference equation, some multilinear generating functions for HnHn are discussed.