Global Solutions of Certain Second-Order Differential Equations with a   High Degree of Apparent Singularity
  Infinitely many explicit solutions of certain second-order differential equations with an apparent singularity of characteristic exponent -2 are constructed by adjusting the parameter of the multi-indexed Laguerre polynomials. 
Ryu Sasaki and Kouichi Takemura
math.CA hep-th math-ph math.MP quant-ph