discuss the relation between Leonard pairs and parameter arrays. In Section \[paawrel\] we recall expressions of the Askey-Wilson coefficients in (\[askwil1\])–(\[askwil2\]) in terms of parameter arrays. Section \[normawrels\] deals with possible normalizations of Askey-Wilson relations. Sections \[qpararrays1\] and \[qpararrays2\] present two normalizations of $q$-parameter arrays and Askey-Wilson relations for them. Section \[otherpararrays\] presents normalizations of other parameter arrays and Askey-Wilson relations for them. In Section \[classifics\] we give a classification of Askey-Wilson relations consistent with the classification of Leonard pairs. In Section \[conclusions\] we discuss uniqueness of normalizations of Leonard pairs and Askey-Wilson relations.

Leonard pairs and parameter arrays {#lsparar}
==================================

Leonard pairs are represented and classified by parameter arrays. More precisely, parameter arrays are in one-to-one correspondence with [*Leonard systems*]{} [@terwgen Definition 3.2], and to each Leonard pair one associates 4 Leonard systems or parameter arrays. From now on, let $d$ be a non-negative integer, and let $V$ be a vector space with dimension $d+1$ over ${{\Bbb K}}$.

[@hartwig] Let $(A,A^*)$ denote a Leonard pair on $V$. Let $W$ denote a vector space over ${{\Bbb K}}$ with finite positive dimension, and let $(B,B^*)$ denote a Leonard pair on $W$. By an [*isomorphism of Leonard pairs*]{} we mean an isomorphism 