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Linear Differential Elimination for Analytic Functions


This paper provides methods to decide whether a given analytic function of several complex variables is a linear combination of finitely many given analytic functions with coefficients of the following special form: Each one of these coefficients is a composition of an unknown analytic function of less arguments than the function to be expressed, with fixed analytic functions. Methods which compute suitable coefficient functions in the affirmative case are presented as well.

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Correspondence to Daniel Robertz.

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Plesken, W., Robertz, D. Linear Differential Elimination for Analytic Functions. Math.Comput.Sci. 4, 231–242 (2010).

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  • Analytic function
  • Differential elimination
  • Functional dependence
  • Linear pde’s
  • Janet basis

Mathematics Subject Classification (2010)

  • Primary 12H05
  • Secondary 13N10