PROPOSED SIAM PROBLEM

BAILEY, DAVID H. ; BORWEIN, JONATHAN M.

Lawrence Berkeley National Laboratory

关键词: Computers;    Bessel Functions;    Mathematics;    97;   

DOI  :  10.2172/983316
RP-ID  :  LBNL-3493E
RP-ID  :  DE-AC02-05CH11231
RP-ID  :  983316

美国|英语

来源: UNT Digital Library

【 摘 要 】

A recent paper by the present authors, together with mathematical physicists David Broadhurst and M. Larry Glasser, explored Bessel moment integrals, namely definite integrals of the general form {integral}{sub 0}{sup {infinity}} t{sup m}f{sup n}(t) dt, where the function f(t) is one of the classical Bessel functions. In that paper, numerous previously unknown analytic evaluations were obtained, using a combination of analytic methods together with some fairly high-powered numerical computations, often performed on highly parallel computers. In several instances, while we were able to numerically discover what appears to be a solid analytic identity, based on extremely high-precision numerical computations, we were unable to find a rigorous proof. Thus we present here a brief list of some of these unproven but numerically confirmed identities.