q-Taylor theorems, polynomial expansions, and interpolation of entire functions Original Research Article

We establish q-analogues of Taylor series expansions in special polynomial bases for functions analytic in bounded domains and for entire functions whose maximum modulus M(r;f) satisfies |ln M(r;f)|⩽A ln2 r. This solves the problem of constructing such entire functions from their values at [aqn+q−n/a]/2, for 0