  We show that a version of dimensional interpolation for the
Riemann--Roch--Hirzebruch formalism in the case of a grassmannian leads to an
expression for the Euler characteristic of line bundles in terms of a Selberg
integral. We propose a way to interpolate higher Bessel equations, their wedge
powers, and monodromies thereof to non--integer orders, and link the result
with the dimensional interpolation of the RRH formalism in the spirit of the
gamma conjectures.
