  The present paper is devoted to power series of SP type, i.e. with
coefficients that are syntactically sum-product combinations. Apart from their
applications to analytic knot theory and the so-called "Volume Conjecture",
SP-series are interesting in their own right, on at least four counts: (i) they
generate quite distinctive resurgence algebras (ii) they are one of those
relatively rare instances when the resurgence properties have to be derived
directly from the Taylor coefficients (iii) some of them produce singularities
that unexpectedly verify finite-order differential equations (iv) all of them
are best handled with the help of two remarkable, infinite-order
integral-differential transforms, "mir" and "nir".
