  On the example of massless QED we study an asymptotic of the vertex when only
one of the two virtualities of the external fermions is sent to zero. We call
this regime the skewed Sudakov regime. First, we show that the asymptotic is
described with a single form factor, for which we derive a linear evolution
equation. The linear operator involved in this equation has a discrete
spectrum. Its eigenfunctions and eigenvalues are found. The spectrum is a
shifted sequence of harmonic numbers. With the spectrum found, we represent the
expansion of the asymptotic in the fine structure constant in terms of multiple
polylogarithms. Using this representation, the exponentiation of the doubly
logarithmic corrections of the Sudakov form factor is recovered. It is pointed
out that the form factor of the skewed Sudakov regime is growing with the
virtuality of a fermion decreasing at a fixed virtuality of another fermion.
