  In this note, we derive explicitly the local relative trace formula for the
symmetric space F*\SL(2,F) at the level of Lie algebras, where F is a p-adic
field of residue characteristic greater than two and F* is the set of
invertible elements in F. This is perhaps one of the simplest non-trivial
analogs of the trace formula, and also a motivating example for the author's
work (in preparation) on the relative trace formula.
