Applicability of multiplicative renormalization method for a certain function

Kubo, Izumi; Kuo, Hui-Hsiung; Namli, Suat

doi:10.31390/cosa.2.3.02

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Classes Of Mrm-applicable Measures For Power Function Of Gen1

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2013

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“…[9][10][11][12] Since the first two cases are extremal and have been discussed in previous papers, we will exclude them in this paper. On the contrary, the case κ = 2 can be included in the general cases.…”

Section: Classes Of Mrm-applicable Measures For Power Function Of Genmentioning

confidence: 99%

Classes of MRM-Applicable Measures for the Power Function of General Order

Kubo

Kuo

Namli

2013

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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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.

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Section: Classes Of Mrm-applicable Measures For Power Function Of Genmentioning

confidence: 99%