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.
Type de document :
Article dans une revue
Research in Number Theory, SpringerOpen, 2017, 3 (1), 〈10.1007/s40993-016-0065-3 〉
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01448646
Contributeur : Christophe Vignat <>
Soumis le : samedi 28 janvier 2017 - 16:16:51
Dernière modification le : jeudi 5 avril 2018 - 12:30:05

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

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