Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
polynomial sequence
|
| gptkbp:application |
gptkb:probability_theory
combinatorics orthogonal polynomials |
| gptkbp:defines |
A sequence of polynomials {P_n(x)} such that d/dx P_n(x) = n P_{n-1}(x)
|
| gptkbp:example |
gptkb:Hermite_polynomials
gptkb:Euler_polynomials gptkb:Bernoulli_polynomials |
| gptkbp:exponentialGeneratingFunction |
A(t)exp(xt) = sum_{n=0}^∞ P_n(x) t^n / n!
|
| gptkbp:field |
gptkb:algebra
gptkb:mathematics analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Appell polynomials
|
| gptkbp:namedAfter |
gptkb:Paul_Émile_Appell
|
| gptkbp:property |
linear recurrence relation
differentiation property exponential generating function |
| gptkbp:relatedTo |
gptkb:Sheffer_sequence
|
| gptkbp:studiedBy |
gptkb:Paul_Émile_Appell
|
| gptkbp:bfsParent |
gptkb:Paul_Appell
|
| gptkbp:bfsLayer |
6
|