Classes of mrm-applicable measures for the power function of general order
The authors have previously studied multiplicative renormalization method (MRM) for generating functions of orthogonal polynomials. In particular, they have determined all MRM-applicable measures for renormalizing functions h(x) = ex, h(x) = (1 - x)-κ, κ = 1/2, 1, 2. For the cases h(x) = ex and (1 - x)-1, there are very large classes of MRM-applicable measures. For the other two cases κ = 1/2, 2, MRM-applicable measures belong to special classes of a certain kind of beta distributions. In this paper, we determine all MRM-applicable measures for h(x) = (1 - x)-κ with κ ≠ 0, 1, 1/2. © 2013 World Scientific Publishing Company.
Publication Source (Journal or Book title)
Infinite Dimensional Analysis, Quantum Probability and Related Topics
Kubo, I., Kuo, H., & Namli, S. (2013). Classes of mrm-applicable measures for the power function of general order. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 16 (4) https://doi.org/10.1142/S0219025713500288