167 research outputs found
Extension of the Bernoulli and Eulerian Polynomials of Higher Order and Vector Partition Function
Following the ideas of L. Carlitz we introduce a generalization of the
Bernoulli and Eulerian polynomials of higher order to vectorial index and
argument. These polynomials are used for computation of the vector partition
function , i.e., a number of integer solutions to a linear
system . It is shown that can be expressed through the vector Bernoulli polynomials of higher order.Comment: 18 page
An Explicit Formula for Restricted Partition Function through Bernoulli Polynomials
Explicit expressions for restricted partition function and
its quasiperiodic components (called Sylvester waves) for a
set of positive integers are derived. The
formulas are represented in a form of a finite sum over Bernoulli polynomials
of higher order with periodic coefficients.Comment: 8 pages, submitted to The Ramanujan Journa
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