▁polynomial , ▁denoted ▁H p , ▁ ▁if ▁it ▁is ▁regular ▁at ▁all ▁three ▁finite ▁singular ▁points   z   =   0 ,   1 ,   a . ▁ ▁He un ' s ▁equation ▁ ▁He un ' s ▁equation ▁is ▁a ▁second - order ▁linear ▁ordinary ▁differential ▁equation ▁( O DE ) ▁of ▁the ▁form ▁ ▁The ▁condition ▁ ▁is ▁needed ▁to ▁ensure ▁regular ity ▁of ▁the ▁point ▁at   ∞ . ▁ ▁The ▁complex ▁number ▁q ▁is ▁called ▁the ▁access ory ▁parameter . ▁He un ' s ▁equation ▁has ▁four ▁regular ▁singular ▁points : ▁ 0 ,   1 ,   a ▁and ▁ ∞ ▁with ▁ex ponents ▁( 0 ,   1   −   γ ), ▁( 0 ,   1   −   δ ), ▁( 0 ,   1   −   ϵ ), ▁and ▁( α ,   β ). ▁Every ▁second - order ▁linear ▁O DE ▁on ▁the ▁extended ▁complex ▁plane ▁with ▁at ▁most ▁four ▁regular ▁singular ▁points , ▁such ▁as ▁the ▁Lam é ▁equation ▁or ▁the ▁hyper ge ometric ▁differential ▁equation , ▁can ▁be ▁transformed ▁into ▁this ▁equation ▁by ▁a ▁change ▁of ▁variable . ▁ ▁q - anal og ▁The ▁q - anal og ▁of ▁He un ' s ▁equation ▁has ▁been ▁discovered ▁by ▁ ▁and ▁studied ▁by ▁. ▁ ▁Sym met ries ▁ ▁He un ' s ▁ ▁equation ▁has ▁a ▁group ▁of ▁symmet ries ▁of ▁order ▁ 1 9 2 , ▁is omorphic ▁to ▁the ▁C ox eter ▁group ▁of