Global Solutions of Certain Second-Order Differential Equations with a High Degree of Apparent Singularity

Abstract

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.

References in corpus (5)

• Orthogonal Polynomials from Hermitian Matrices
• Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states
• Exact solution in the Heisenberg picture and annihilation-creation operators
• Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations
• Classification of Fuchsian systems and their connection problem

Cited by in corpus (1)

• Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials