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.
Document type :
Journal articles
Complete list of metadatas

https://hal-centralesupelec.archives-ouvertes.fr/hal-01448646
Contributor : Christophe Vignat <>
Submitted on : Saturday, January 28, 2017 - 4:16:51 PM
Last modification on : Monday, November 26, 2018 - 4:12:54 PM

Links full text

Identifiers

Citation

Karl Ditcher, 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⟩

Share

Metrics

Record views

364