Divided differences and a general explicit formula for sequences of Mansour–Mulay–Shattuck

Divided differences is a very important tool, often used both in theory and in practice, for the approximation of functions. In this paper, we employ divided differences with repetitions to find a general explicit formula for the sequences satisfying Mansour–Mulay–Shattuck’s two-term recurrence with arbitrary (bi)i⩾0(bi)i⩾0.