Q-of Mahler Expansions In Z_p Consistent Continuity

(?)form an orthonormal base (the "Mahler base") of C(Z_pâ†'K),and we can deduce that (?) formbases of C(Z_pâ†'K).Assume |q - 1|＜(?),then we can prove that f(x) =(?)∈C(Z_pâ†'K) is a C¹- function if and only if (?) |c_n,q|n = 0.