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An explicit form of the polynomial part of a restricted partition function

Abstract : We prove an explicit formula for the polynomial part of a restricted partition function, also known as the first Sylvester wave. This is achieved by way of some identities for higher-order Bernoulli polynomials, one of which is analogous to Raabe’s well-known multiplication formula for the ordinary Bernoulli polynomials. As a consequence of our main result we obtain an asymptotic expression of the first Sylvester wave as the coefficients of the restricted partition grow arbitrarily large.
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Contributor : Christophe Vignat Connect in order to contact the contributor
Submitted on : Saturday, January 28, 2017 - 4:16:51 PM
Last modification on : Saturday, May 1, 2021 - 3:48:38 AM

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Karl Dilcher, Christophe Vignat. An explicit form of the polynomial part of a restricted partition function. Research in Number Theory, Springer, 2017, 3 (1), ⟨10.1007/s40993-016-0065-3⟩. ⟨hal-01448646⟩

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