On higher-order flavour-singlet splitting and coefficient functions at large x

We discuss the large-x behaviour of the splitting functions Pqg and Pgq and of flavour-singlet coefficient functions, such as the gluon contributions C2,g and CL,g to the structure functions F2,L, in massless perturbative QCD. These quantities are suppressed by one or two powers of (1−x) with respect to the (1−x)−1 terms which are the subject of the well-known threshold exponentiation. We show that the double-logarithmic contributions to Pqg, Pgq and CL at order αs4 can be predicted from known third-order results and present, as a first step towards a full all-order generalization, the leading-logarithmic large-x behaviour of Pqg, Pgq and C2,g at all orders in αs.