<ul><li>The discrete Taylor series is a notation that simplifies Newton’s interpolation formula and suggests extensions.</li><li>The notation involves the forward difference operator Δ and falling powers denoted by a bar under the exponent.</li><li>Newton’s formula is a discrete analog of Taylor’s formula and applies to polynomials using only finite operations.</li><li>The convergence of the infinite series in Newton’s formula is explored, and conditions for convergence are discussed.</li></ul>

Discrete Taylor series

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