Umbral Taylor Series
Similar relationships were also observed in the theory of finite differences. The umbral version of the Taylor series is given by a similar expression involving the k 'th forward differences of a polynomial function f,
where
is the Pochhammer symbol used here for the falling sequential product. A similar relationship holds for the backward differences and rising factorial.
This series is also known as the Newton series or Newton's forward difference expansion. The analogy to Taylor's expansion is utilized in the Calculus of finite differences.
Read more about this topic: Umbral Calculus
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