following result [@TerwVid Theorem 1.5].

\[lptheorem\] Let $V$ denote a vector space over ${{\Bbb K}}$ with finite positive dimension. Let $(A,A^*)$ be a Leonard pair on $V$. Then there exists a sequence of scalars $\beta,\gamma,\gamma^*,\varrho,\varrho^*$, $\omega,\eta,\eta^*$ taken from ${{\Bbb K}}$ such that $$\begin{aligned}
  \label{askwil1}
A^2 A^*-\beta A A^*\!A+A^*\!A^2-\gamma\left( A A^*\!+\!A^*\!A
\right)-\varrho\,A^* {&\!\!\!=\!\!\!&}\gamma^*\!A^2+\omega A+\eta\,I,\\
\label{askwil2} A^*{}^2\!A-\beta A^*\!AA^*\!+AA^*{}^2-
\gamma^*\!\left(A^*\!A\!+\!A A^*\right)-\varrho^*\!A {&\!\!\!=\!\!\!&}\gamma
A^*{}^2+\omega A^*\!+\eta^*I.\end{aligned}$$ The sequence is uniquely determined by the pair $(A,A^*)$ provided the dimension of $V$ is at least $4$.

The equations (\[askwil1\])–(\[askwil2\]) are called the [*Askey-Wilson relations*]{}. They first appeared in the work [@Zhidd] of Zhedanov, where he showed that the Askey-Wilson polynomials give pairs of infinite-dimensional matrices which satisfy the Askey-Wilson relations. We denote this pair of equations by $AW(\beta,\gamma,\gamma^*,\varrho,\varrho^*,\omega,\eta,\eta^*)$.

It is easy to notice that if $(A,A^*)$ is a Leonard pair, then $$\label{translation}
(tA+c,\,t^*\!A^*\!+c^*),\qquad \mbox{with}\ c,c^*,t,t^*\!\in{{\Bbb K}}\mbox{ and }
t,t^*\neq 0,$$ is a Leonard pair as well. We say that the two Leonard pairs are related by the [*affine transformation*]{} $(A,A^*)\mapsto
(tA+c,\,t^*\!A^*\!+c^*)$. Affine transformations act on Askey-Wilson relations as well, as explained in Section \[normawrels\] below. For example, if then the Askey-Wilson relations can be normalized so that $\gamma=0$ and . Affine transformations can be used to normalize 