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- Stirling_transform abstract "In combinatorial mathematics, the Stirling transform of a sequence { an : n = 1, 2, 3, ... } of numbers is the sequence { bn : n = 1, 2, 3, ... } given bywhere is the Stirling number of the second kind, also denoted S(n,k) (with a capital S), which is the number of partitions of a set of size n into k parts.The inverse transform iswhere s(n,k) (with a lower-case s) is a Stirling number of the first kind.Berstein and Sloane (cited below) state "If an is the number of objects in some class with points labeled 1, 2, ..., n (with all labels distinct, i.e. ordinary labeled structures), then bn is the number of objects with points labeled 1, 2, ..., n (with repetitions allowed)."Ifis a formal power series (note that the lower bound of summation is 1, not 0), andwith an and bn as above, then".
- Stirling_transform wikiPageID "1782555".
- Stirling_transform wikiPageRevisionID "547488470".
- Stirling_transform hasPhotoCollection Stirling_transform.
- Stirling_transform subject Category:Factorial_and_binomial_topics.
- Stirling_transform subject Category:Transforms.
- Stirling_transform comment "In combinatorial mathematics, the Stirling transform of a sequence { an : n = 1, 2, 3, ... } of numbers is the sequence { bn : n = 1, 2, 3, ...".
- Stirling_transform label "Stirling transform".
- Stirling_transform sameAs m.05wj88.
- Stirling_transform sameAs Q7617600.
- Stirling_transform sameAs Q7617600.
- Stirling_transform wasDerivedFrom Stirling_transform?oldid=547488470.
- Stirling_transform isPrimaryTopicOf Stirling_transform.