MRM-applicable orthogonal polynomials for certain hypergeometric functions

Kubo, Izumi; Kuo, Hui-Hsiung

doi:10.31390/cosa.3.3.05

Cited by 3 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The following Lemmas 2.1, 2.2 and 2.6 are shown in [9]. Lemmas 2.3 and 2.4 are in [10]. Other lemmas are easily seen.…”

Section: Some Lemmasmentioning

confidence: 99%

Twin MRM-triples in multiplicative renormalization method

Kubo¹,

Kuo²

2011

COSA

Self Cite

View full text Add to dashboard Cite

MRM-applicable measures for MRM-factors 0 F 0 (−; −; x) = e x , 1 F 0 (κ; −; x) = (1 − x) −κ and 1 F 1 (1; 2; x) = 1 x (e x − 1) have already been completely determined. Conversely, MRM-factors for which those measures are MRM-applicable have also been completely determined. Some measures have couples of MRM-triples h(x), ρ(t), B(t) and h 0 (x), ρ 0 (t), B 0 (t) such that h 0 (x) = d dx xh(x) , B(t) = 1 t ρ(t), ρ 0 (t) = ρ(t), B 0 (t) = ρ (t) = d dt tB(t). Such triples are called twin MRM-triples. We determine in this paper all twin MRM-triples for symmetric measures and for measures with the Jacobi-Szegö parameters αn = a 2 n 2 + a 1 n + a 0 .

show abstract

“…The following Lemmas 2.1, 2.2 and 2.6 are shown in [9]. Lemmas 2.3 and 2.4 are in [10]. Other lemmas are easily seen.…”

Section: Some Lemmasmentioning

confidence: 99%

Twin MRM-triples in multiplicative renormalization method

Kubo¹,

Kuo²

2011

COSA

Self Cite

View full text Add to dashboard Cite

show abstract

“…An analysis of the connections between orthogonal polynomials and probability distributions via properties of their generating function are accomplished in [1,14].…”

Section: Introductionmentioning

confidence: 99%

Krawtchouk-Griffiths systems II: as Bernoulli systems

Feinsilver¹

2016

COSA

View full text Add to dashboard Cite

We call Krawtchouk-Griffiths systems, KG-systems, systems of multivariate polynomials orthogonal with respect to corresponding multinomial distributions. The original Krawtchouk polynomials are orthogonal with respect to a binomial distribution. Here we present a Fock space construction with raising and lowering operators. The operators of "multiplication by X" are found in terms of boson operators and corresponding recurrence relations presented. The Riccati partial differential equations for the differentiation operators, Berezin transform and associated partial differential equations are found. These features provide the specifications for a Bernoulli system as a quantization formulation of multivariate Krawtchouk polynomials.

show abstract