Polynomial solutions of differential equations

  title={Polynomial solutions of differential equations},
  author={H Azad and Abdallah Laradji and M. T. Mustafa},
k=0 ak(x)y , where ak is a polynomial of degree ≤ k, over an infinite field F has all eigenvalues in F in the space of polynomials of degree at most n, for all n. If these eigenvalues are distinct, then there is a unique monic polynomial of degree n which is an eigenfunction of the operator L, for every non-negative integer n. Specializing to the real field, the potential of the method is illustrated by recovering Bochner’s classification of second order ODEs with polynomial coefficients and… CONTINUE READING


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