Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
A sequence of polynomials (S_n(x)) such that S_0(x) = c ≠ 0 and S_n(x) has degree n for all n ≥ 0, and satisfies a binomial-type identity.
|
| gptkbp:example |
gptkb:Laguerre_polynomials
gptkb:Hermite_polynomials gptkb:Bernoulli_polynomials |
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:hasApplication |
gptkb:probability_theory
orthogonal polynomials enumerative combinatorics umbral calculus |
| gptkbp:hasSubfield |
combinatorics
umbral calculus |
| https://www.w3.org/2000/01/rdf-schema#label |
Sheffer sequence
|
| gptkbp:introduced |
gptkb:Isador_M._Sheffer
|
| gptkbp:introducedIn |
1939
|
| gptkbp:namedAfter |
gptkb:Isador_M._Sheffer
|
| gptkbp:property |
Sheffer sequences generalize binomial type polynomial sequences.
Sheffer sequences are characterized by a generating function of the form A(t)exp(xB(t)), with A(0) ≠ 0, B(0) = 0, B'(0) ≠ 0. Every binomial type sequence is a Sheffer sequence. |
| gptkbp:relatedTo |
gptkb:Appell_sequence
binomial type polynomial sequence |
| gptkbp:bfsParent |
gptkb:Appell_polynomials
|
| gptkbp:bfsLayer |
7
|