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Shape invariant supersymmetric partner potentials corresponding to
the Natanzon superpotential $Atanh \gamma r - B \hspace{0.1cm}
coth \gamma r $ and its twin i.e. $-(A + B)tanh \gamma r - B
\hspace{0.1cm} sech \gamma r \hspace{0.1cm} csch \gamma r$ are
obtained as 2-fold hierarchies whose solutions are a common set of
the quantum states. It is shown that they are derived by using
simultaneous laddering relations with respect to two different
parameters n and m of some associated Gegenbauer functions via two
different methods including (a) simultaneous increasing or
decreasing of the parameters, and (b) increasing one of the
parameters and decreasing the other one. The shape invariance
condition in the concept of Gendenshtein on the 2-fold hierarchies
of supersymmetric partner potentials with respect to the
parameters n and m is inherited from those laddering relations by
two different ways.
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