We introduce a method for computing the sum of a series of the form \(\sum _{m=1}^{\infty }a_mJ^{(3)}_{\mu }(qj_{m,\nu }x;q^2)\) , where \((j_{m,\nu })_m,\) are the positive zeros of the third Jackson q-Bessel function \(J^{(3)}_{\mu }(\cdot ;q^2)\) arranged in increasing order of magnitude. The method allows us to calculate the sum of the series assuming that the sum is known for a particular value, \(\eta \) of the parameter \(\mu \) . We used the method to generalize some known identities. We also introduced similar results for series involving second Jackson q-Bessel functions and certain generalizations of identities involving q-special functions.