(Scaling equation 3) Let be an MRA and is the auxiliary function (as in the definition ( Scaling filter and auxiliary function )). Then the function satisfies the relationship

According to the proposition ( OST property 1 ), we have for We use the proposition ( Scaling equation ). We separate even and odd -terms. According to the definition of , see the proposition ( Scaling equation ), . We use the proposition ( OST property 1 ) again.