  The paper studies violation of conventional rules of SUSY quantum mechanics
for the centrifugal potential V(r) within the limit-circle (LC) range. A
special attention is given to transformation properties of the Titchmarsh-Weyl
m-function under Darboux deformations of the reflective Kratzer oscillator:
centrifugal Kepler-Coulomb (KC) potential plus a Taylor series in r. Since our
analysis is based on Fulton's representation of a regular-at-infinity solution
[Math. Nachr. 281, 1418 (2008)] as a superposition of two Frobenius solutions
at the origin, we refer to the appropriate expressions as the
Titchmarsh-Weyl-Fulton (TWF) functions. Explicit transformation relations are
derived for partner TWF functions associated with SUSY pairs of centrifugal
potentials. It is shown that these relations have a completely different form
for Darboux transformations (DTs) keeping the potential within the LC range.
  As an illustration, we use regular nodeless Frobenius solutions to construct
SUSY partners of the radial r- and c-Gauss-reference (GRef) potentials solvable
via hypergeometric and confluent hypergeometric functions, respectively. We
explicitly demonstrate existence of non-isospectral partners of both radial
potentials in the LC region and obtain their discrete energy spectra using the
derived closed-form expressions for the TWF functions. The general
transformation relations for the TWF function have been verified taking
advantage of form-invariance of the radial GRef potentials under double-step
DTs with the so-called 'basic' seed solutions (SSs). Similarly we directly
ratify that TWF functions for three shape-invariant reflective potentials on
the half-line -- hyperbolic Poschl-Teller (h-PT), Eckart/Manning-Rosen (E/MR),
and centrifugal KC potentials - do retain their form under basic DTs.
