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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