2013/09/29 by Kouba, Omran
#11B68 #11L03 #30D10 #32B05 #42A16 #43E05 #65D32 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.1309.7560
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications to these polynomials are presented, including a unified approach to the asymptotic expansion of the error term in many numerical quadrature formulae, and many new and sharp inequalities, that bound some trigonometric sums.