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In mathematics, an Appell sequence, named after Paul Émile Appell, is any polynomial sequence ''n'' = 0, 1, 2, ... satisfying the identity : and in which ''p''0(''x'') is a non-zero constant. Among the most notable Appell sequences besides the trivial example are the Hermite polynomials, the Bernoulli polynomials, and the Euler polynomials. Every Appell sequence is a Sheffer sequence, but most Sheffer sequences are not 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 ''p''0(''x'') is a non-zero constant; * For some sequence ''n'' = 0, 1, 2, ... of scalars with ''c''0 ≠ 0, :: * For the same sequence of scalars, :: :where :: * For ''n'' = 0, 1, 2, ..., :: 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Appell sequence」の詳細全文を読む スポンサード リンク
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