  We state a generalization of the Connes-Tretkoff-Moscovici Rearrangement
Lemma and give a surprisingly simple (almost trivial) proof of it. Secondly, we
put on a firm ground the multivariable functional calculus used implicitly in
the Rearrangement Lemma and elsewhere in the recent modular curvature paper by
Connes and Moscovici. Furthermore, we show that the fantastic formulas
connecting the one and two variable modular functions of loc. cit. are just
examples of the plenty recursion formulas which can be derived from the
calculus of divided differences. We show that the functions derived from the
main integral occurring in the Rearrangement Lemma can be expressed in terms of
divided differences of the Logarithm, generalizing the "modified Logarithm" of
Connes-Tretkoff.
  Finally, we show that several expansion formulas related to the Magnus
expansion have a conceptual explanation in terms of a multivariable functional
calculus applied to divided differences.
