Poly-Bernoulli number (original) (raw)
Inom matematiken är polybernoullitalen, introducerade av , tal som definieras som där Li är polylogaritmen. är de vanliga Bernoullitalen. Två intressanta formler av Kaneko är och där Stirlingtalen av andra ordningen.
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| dbo:abstract | In mathematics, poly-Bernoulli numbers, denoted as , were defined by M. Kaneko as where Li is the polylogarithm. The are the usual Bernoulli numbers. Moreover, the Generalization of Poly-Bernoulli numbers with a,b,c parameters defined as follows where 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. Also it is the number of open tours by a biased rook on a board (see for definition). The Poly-Bernoulli number satisfies the following asymptotic: For a positive integer n and a prime number p, the poly-Bernoulli numbers satisfy which can be seen as an analog of Fermat's little theorem. Further, the equation has 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 . (en) Inom matematiken är polybernoullitalen, introducerade av , tal som definieras som där Li är polylogaritmen. är de vanliga Bernoullitalen. Två intressanta formler av Kaneko är och där Stirlingtalen av andra ordningen. (sv) |
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| rdfs:comment | Inom matematiken är polybernoullitalen, introducerade av , tal som definieras som där Li är polylogaritmen. är de vanliga Bernoullitalen. Två intressanta formler av Kaneko är och där Stirlingtalen av andra ordningen. (sv) In mathematics, poly-Bernoulli numbers, denoted as , were defined by M. Kaneko as where Li is the polylogarithm. The are the usual Bernoulli numbers. Moreover, the Generalization of Poly-Bernoulli numbers with a,b,c parameters defined as follows where 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). The Poly-Bernoulli number satisfies the following asymptotic: For a positive integer n and a prime number p, the poly-Bernoulli numbers satisfy (en) |
| rdfs:label | Poly-Bernoulli number (en) Polybernoullital (sv) |
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