Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
polynomial sequence
|
| gptkbp:definedIn |
generating function
|
| gptkbp:degree |
n (nth Euler polynomial has degree n)
|
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:firstAppearance |
18th century
|
| gptkbp:generatingFunction |
2e^{xt}/(e^t+1) = sum_{n=0}^∞ E_n(x) t^n/n!
|
| gptkbp:hasSpecialCase |
E_n(0) = Euler numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
Euler polynomials
|
| gptkbp:namedAfter |
gptkb:Leonhard_Euler
|
| gptkbp:notation |
E_n(x)
|
| gptkbp:recurrence |
E_n(x) = E_n(x-1) + n x^{n-1}
|
| gptkbp:relatedTo |
gptkb:Bernoulli_polynomials
gptkb:Euler_numbers |
| gptkbp:usedIn |
analysis
number theory combinatorics |
| gptkbp:bfsParent |
gptkb:Bernoulli_polynomials
|
| gptkbp:bfsLayer |
6
|