아핀 q-크라우트추크 다항식

수학에서 아핀 q-Krawtchouk 다항식은 칼리츠와 호지스가 도입한 기본 아스키 체계에서 기초초기하 직교 다항식 계열이다.로엘로프 코에코크, 피터 A.레스키, 레네 F.스와르투우(2010, 14)는 그들의 재산에 대한 상세한 목록을 제공한다.

정의

다항식은 다음과 같이 기본 초기하 함수의 측면에서 주어진다.

K_{n}^{\text{aff}}(q^{-x};p;N;q)={}_{3}\phi _{2}\left({\begin{matrix}q^{-n},0,q^{-x}\\pq,q^{-N}\end{matrix}};q,q\right),\qquad n=0,1,2,\ldots ,N.

q-Krawtchouk 다항식 → little q-Laguerre 다항식:

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

→

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

= K

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

(

q

x

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

;

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

,

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

∣

q

)

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

= p (

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

;

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

,

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

)

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

= p (

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

x ; p ) = p (q

\lim _{a\to 1}=K_{n}^{\text{aff}}(q^{x-N};p,N\mid q)=p_{n}(q^{x};p,q)

x; p ){a

\to 1}=K_{n}^{

n}^{

n}^{n\mid q^{n

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