The q-Laguerre Polynomials and Related Moment Problems

We study two indeterminate Hamburger moment problems associated with q- Laguerre polynomials. The coefficients in their recurrence relations are of exponential growth. This completes earlier work started by D. Moak. Some of the measures that the polynomials are orthogonal with respect to are found and lead to the evaluation of certain integrals. A symmetric set of orthogonal polynomials is also considered.