  The hyperfine structure (HFS) of a bound electron is modified by the
self-interaction of the electron with its own radiation field. This effect is
known as the self-energy correction. In this work, we discuss the evaluation of
higher-order self-energy corrections to the HFS of bound P states. These are
expressed in a semi-analytic expansion involving powers of Zalpha and
ln(Zalpha), where Z is the nuclear charge number and alpha is the
fine-structure constant. We find that the correction of relative order alpha
(Zalpha)^2 involves only a single logarithm ln(Zalpha) for P_1/2 states [but no
term of order alpha (Zalpha)^2 ln^2(Zalpha), whereas for P_3/2 states, even the
single logarithm vanishes. By a Foldy-Wouthuysen transformation, we identify a
nuclear-spin dependent correction to the electron's transition current, which
contributes to the HFS of P states. A comparison of the obtained analytic
results to a numerical approach is made.
