Classes of mrm-applicable measures for the power function of general order
Document Type
Article
Publication Date
12-1-2013
Abstract
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
Recommended Citation
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