End IntegralChar.
Section MoreIntegralChar.
Implicit Type gT : finGroupType.

(* This is Isaacs, Problem (3.7). *)
Lemma gring_classM_coef_sum_eq gT (G : {group gT}) j1 j2 k g1 g2 g :
let a := @gring_classM_coef gT G j1 j2 in let a_k := a k in
g1 \in enum_val j1 -> g2 \in enum_val j2 -> g \in enum_val k ->
let sum12g := \sum_i 'chi[G]_i g1 * 'chi_i g2 * ('chi_i g)^* / 'chi_i 1%g in
a_k%:R = (#|enum_val j1| * #|enum_val j2|)%:R / #|G|%:R * sum12g.