Friday, May 4, 2012

1205.0712 (Ramos Arturo)

On the compatibility condition for the new translational shape invariant

Ramos Arturo
Motivated by work by Quesne on the one hand and Bougie, Gangopadhyaya and Mallow on the other it has been introduced in a recent article [Ramos A 2011 {\it J. Phys. A: Math. Theor.} {\bf 44} 342001] the notion of compatibility condition for the terms of the superpotential present in those cases. In this paper it is proved that such compatibility condition implies in particular the usual shape invariance condition, and it is in principle applicable to the recent examples of Odake and Sasaki as well (infinitely many polynomial, continuous $l$ and multi-index rational extensions). As a byproduct, we obtain new relations for Laguerre, Jacobi polynomials and (confluent) hypergeometric functions.
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