$\theta^*_0=-\frac{d}2$, $s=1$, $s^*\!=1$. In the Bannai-Ito case, we substitute $$\textstyle
s\mapsto d+1-2u,\quad s^*\!\mapsto d+1-2u^*,\quad r_1\mapsto
u+u^*+v-\frac{d+1}2, $$ so that $r_2\mapsto u+u^*-v-\frac{d+1}2$, and adjust $\theta_0=u-\frac{d}2$, $\theta^*_0=u^*\!-\frac{d}2$, $h=\frac12$, $h^*\!=\frac12$. [$\Box$]{}

\[awnormals2\] Let $u,u^*,v$ denote the same scalar parameters as in the previous lemma. The Askey-Wilson relations for the parameter arrays of Lemma $\ref{normlps2}$ are:

-   For the Racah case: $$\begin{aligned}
    &&\hspace{-24pt}
    AW\big(2,\,2,\,2,\,0,\,0,-2u^2-2u^*{}^2\!-2v^2-2(d\!+\!1)(u+u^*+v)-2d^2-4d,\nonumber\\
    &&2\,u\left(u+d+1\right)\left(v-u^*\right)\left(v+u^*+d+1\right), \\
    &&2\,u^*\!\left(u^*\!+d+1\right)\left(v-u\right)\left(v+u+d+1\right)\big).\nonumber\end{aligned}$$

-   For the Hahn case: $$\begin{aligned}
    \textstyle
    AW\big(2,\,0,\,2,\,1,\,0,\,0,\,-(u^*\!+1)(u^*\!+d)-2v^2-\frac{d^2}2,\,-4u^*(u^*\!+d+1)v\big).\end{aligned}$$

-   For the dual Hahn case: $$\begin{aligned}
    \textstyle
    AW\big(2,\,2,\,0,\,0,\,1,\,0,\,\,-4u(u+d+1)\,v,\,-(u+1)(u+d)-2v^2-\frac{d^2}2\big).\end{aligned}$$

-   For the Krawtchouk case: $$AW\big(2,\,0,\,0,\,1,\,1,\,2v-1,\,0,\,0\big).$$

-   For the Bannai-Ito case, if $d$ is even: $$AW\big(-2,\,0,\,0,\,1,\,1,\,4uu^*\!-2(d\!+\!1)\,v,\,2uv-(d\!+\!1)\,u^*,\,2u^*v-(d\!+\!1)\,u\big).$$

-   For the Bannai-Ito case, if $d$ is odd: $$\begin{aligned}
    &&\hspace{-24pt}\textstyle AW\big(-2,\,0,\,0,\,1,\,1,\,
    -2u^2-2u^*{}^2+2v^2+\frac{(d+1)^2}2, \nonumber \\
    &&\textstyle
    -u^2+u^*{}^2-v^2+\frac{(d+1)^2}4,\,u^2\!-u^*{}^2\!-v^2\!+\frac{(d+1)^2}4\big).\end{aligned}$$

[[**Proof.** ]{}]{}Direct computations with formulas (\[betap1\])–(\[asipq2\]).[$\Box$]{}

\[orphan\] In the characteristic 2, the normalization of part 1 in Lemma \[normrules\] is not available, hence our results are incomplete if char ${{\Bbb K}}=2$. In particular, we miss the orphan case (with char ${{\Bbb K}}=2$ and $d=3$) completely. A general parameter array of the orphan type can be normalized as follows: $$\begin{aligned}
\left(\theta_0,\theta_1,\theta_2,\theta_3\right){&\!\!\!=\!\!\!&}\left(0,\,s+1,\,1,\,s\right),\\
\left(\theta^*_0,\theta^*_1,\theta^*_2,\theta^*_3\right){&\!\!\!=\!\!\!&}\left(0,\,s^*\!+1,\,1,\,s^*\right),\\
\left(\varphi_1,\varphi_2,\varphi_3\right){&\!\!\!=\!\!\!&}\left(r,\,1,\,r+s+s^*\right),\\
\left(\phi_1,\phi_2,\phi_3\right){&\!\!\!=\!\!\!&}\left(r+s+s\,s^*,\,1,\,r+s^*\!+s\,s^*\right).\end{aligned}$$ Here adjusted $\theta_0=0$, $\theta^*_0=0$, $h=1$, $h^*=1$ in [@terwgen Example 35.14]. The Askey-Wilson relations are $$\label{orphanaw}
AW(0,\,1,\,1,\,s^2+s,\,s^*{}^2+s^*,\,s\,s^*,\,r\,s,\,r\,s^*).$$ The relations can be renormalized to $\rho=0$, $\rho^*=0$ 