Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
polynomial sequence |
| gptkbp:application |
differentiation of composite functions
moments and cumulants in probability theory |
| gptkbp:defines |
sum over all partitions of n of products of x_k
|
| gptkbp:field |
mathematical analysis
combinatorics |
| gptkbp:first_terms |
B_0 = 1
|
| gptkbp:generatingFunction |
exp(sum_{k=1}^∞ x_k t^k / k!)
|
| gptkbp:hasSpecialCase |
Bell numbers when x_k = 1 for all k
|
| https://www.w3.org/2000/01/rdf-schema#label |
complete Bell polynomials
|
| gptkbp:namedAfter |
gptkb:Eric_Temple_Bell
|
| gptkbp:notation |
B_n(x_1, x_2, ..., x_n)
|
| gptkbp:OEIS |
A099594
|
| gptkbp:recurrence |
B_{n+1}(x_1,...,x_{n+1}) = sum_{k=0}^n (n choose k) B_{n-k}(x_1,...,x_{n-k}) x_{k+1}
|
| gptkbp:relatedTo |
gptkb:Bell_numbers
partial Bell polynomials |
| gptkbp:seeAlso |
gptkb:exponential_polynomials
gptkb:Stirling_numbers_of_the_second_kind |
| gptkbp:usedFor |
gptkb:Faà_di_Bruno's_formula
partitioning sets |
| gptkbp:variant |
n
x_1 x_2 x_k |
| gptkbp:bfsParent |
gptkb:Bell_polynomials
|
| gptkbp:bfsLayer |
6
|