Appell Sequence - Equivalent Characterizations of Appell Sequences

Equivalent Characterizations of Appell Sequences

The following conditions on polynomial sequences can easily be seen to be equivalent:

  • For n = 1, 2, 3, ...,
and p0(x) is a non-zero constant;
  • For some sequence {cn}n = 0, 1, 2, ... of scalars with c0 ≠ 0,
  • For the same sequence of scalars,
where
  • For n = 0, 1, 2, ...,

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