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CLASSES OF MRM-APPLICABLE MEASURES FOR THE POWER FUNCTION OF GENERAL ORDER

IZUMI KUBO

Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan

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HUI-HSIUNG KUO

Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA

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SUAT NAMLI

North American College, 3203 N Sam Houston Pkwy W, Houston, TX 77038, USA

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https://doi.org/10.1142/S0219025713500288Cited by:0 (Source: Crossref)

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) = e^x, h(x) = (1 - x)^-κ, κ = 1/2, 1, 2. For the cases h(x) = e^x 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.

Keywords:

AMSC: 33C45, 60E05, 33D45, 44A15

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