In this paper, we present q-Bernoulli and q-Euler polynomials generated by the third Jackson q-Bessel function to construct new types of q-Lidstone expansion theorem. We prove that the entire function may be expanded in terms of q-Lidstone polynomials which are q-Bernoulli polynomials and the coefficients are the even powers of the q-derivative δq f (z) δq z at 0 and 1. The other forms expand the function in q-Lidstone polynomials based on q-Euler polynomials and the coefficients contain the even and odd powers of the q-derivative δq f (z) δq z .
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