Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
polynomial sequence
|
| gptkbp:application |
gptkb:Euler–Maclaurin_formula
gptkb:Faulhaber's_formula summation of powers |
| gptkbp:definedIn |
generating function
|
| gptkbp:differential |
yes
|
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:first_terms |
B_0(x) = 1
|
| gptkbp:hasSpecialCase |
B_n(0) = Bernoulli number B_n
B_n(1) = (-1)^n B_n |
| https://www.w3.org/2000/01/rdf-schema#label |
Bernoulli polynomials
|
| gptkbp:namedAfter |
gptkb:Jacob_Bernoulli
|
| gptkbp:notation |
B_n(x)
|
| gptkbp:orthogonality |
not orthogonal
|
| gptkbp:recurrence |
B_n'(x) = n B_{n-1}(x)
|
| gptkbp:relatedTo |
gptkb:Bernoulli_numbers
gptkb:Euler_polynomials |
| gptkbp:sequence |
gptkb:A027641
|
| gptkbp:usedIn |
analysis
number theory combinatorics |
| gptkbp:bfsParent |
gptkb:Hurwitz_zeta_function
|
| gptkbp:bfsLayer |
5
|