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- Poly-Bernoulli_number abstract "In mathematics, poly-Bernoulli numbers, denoted as , were defined by M. Kaneko aswhere Li is the polylogarithm. The are the usual Bernoulli numbers.Moreover, the Generalization of Poly-Bernoulli numbers with a,b,c parameters defined by Hassan Jolany as followswhere Li is the polylogarithm. Kaneko also gave two combinatorial formulas:where is the number of ways to partition a size set into non-empty subsets (the Stirling number of the second kind).A combinatorial interpretation is that the poly-Bernoulli numbers of negative index enumerate the set of by (0,1)-matrices uniquely reconstructible from their row and column sums.For a positive integer n and a prime number p, the poly-Bernoulli numbers satisfywhich can be seen as an analog of Fermat's little theorem. Further, the equationhas no solution for integers x, y, z, n > 2; an analog of Fermat's last theorem.Moreover, there is an analogue of Poly-Bernoulli numbers(like Bernoulli numbers and Euler numbers) which is known as Poly-Euler numbersPoly-Bernoulli numbers have the same duality which known as Poly-Euler numbers".
- Poly-Bernoulli_number wikiPageExternalLink 1109.1387.
- Poly-Bernoulli_number wikiPageExternalLink vol8.html.
- Poly-Bernoulli_number wikiPageExternalLink thesis.pdf.
- Poly-Bernoulli_number wikiPageID "3492608".
- Poly-Bernoulli_number wikiPageRevisionID "606798810".
- Poly-Bernoulli_number hasPhotoCollection Poly-Bernoulli_number.
- Poly-Bernoulli_number subject Category:Enumerative_combinatorics.
- Poly-Bernoulli_number subject Category:Integer_sequences.
- Poly-Bernoulli_number type Abstraction100002137.
- Poly-Bernoulli_number type Arrangement107938773.
- Poly-Bernoulli_number type Group100031264.
- Poly-Bernoulli_number type IntegerSequences.
- Poly-Bernoulli_number type Ordering108456993.
- Poly-Bernoulli_number type Sequence108459252.
- Poly-Bernoulli_number type Series108457976.
- Poly-Bernoulli_number comment "In mathematics, poly-Bernoulli numbers, denoted as , were defined by M. Kaneko aswhere Li is the polylogarithm. The are the usual Bernoulli numbers.Moreover, the Generalization of Poly-Bernoulli numbers with a,b,c parameters defined by Hassan Jolany as followswhere Li is the polylogarithm.".
- Poly-Bernoulli_number label "Poly-Bernoulli number".
- Poly-Bernoulli_number sameAs m.09ggpb.
- Poly-Bernoulli_number sameAs Q7226095.
- Poly-Bernoulli_number sameAs Q7226095.
- Poly-Bernoulli_number sameAs Poly-Bernoulli_number.
- Poly-Bernoulli_number wasDerivedFrom Poly-Bernoulli_number?oldid=606798810.
- Poly-Bernoulli_number isPrimaryTopicOf Poly-Bernoulli_number.