  The article describes interesting nonlinear differential identities satisfied
by standard exponential and trigonometric functions, which appeared as
byproducts of medical imaging research. They look like some kind of
non-commutative binomial formulas. A brief description of the origin of these
identities is provided, as well as their direct algebraic derivation. Relations
with separate analyticity theorems in several complex variables and some open
problems are also mentioned.
