Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
orthogonal polynomials
|
| gptkbp:affiliatedWith |
gptkb:Askey_scheme
|
| gptkbp:application |
gptkb:probability_theory
mathematical physics combinatorics |
| gptkbp:definedIn |
discrete variable
|
| gptkbp:degree |
n
|
| gptkbp:domain |
x = 0, 1, 2, ...
|
| gptkbp:hasSpecialCase |
gptkb:Meixner–Pollaczek_polynomials
|
| https://www.w3.org/2000/01/rdf-schema#label |
Meixner polynomials
|
| gptkbp:hypergeometricRepresentation |
2F1(-n,-x;beta;1-1/c)
|
| gptkbp:introducedIn |
1934
|
| gptkbp:namedAfter |
gptkb:Josef_Meixner
|
| gptkbp:orthogonalWithRespectTo |
gptkb:negative_binomial_distribution
|
| gptkbp:parameter |
beta
c |
| gptkbp:recurrence |
M_{n+1}(x) = [((c-1)x + (n + beta)c)M_n(x) - n(c-1)cM_{n-1}(x)] / [c(n+1)]
|
| gptkbp:relatedTo |
gptkb:Charlier_polynomials
Krawtchouk polynomials |
| gptkbp:satisfies |
three-term recurrence relation
|
| gptkbp:weight |
(c^x * (beta)_x) / x!
|
| gptkbp:bfsParent |
gptkb:Josef_Meixner
gptkb:Meixner–Pollaczek_polynomials |
| gptkbp:bfsLayer |
6
|