A Contribution to the Theory of Linear Homogeneous Geometric Difference Equations (Q-Difference Equations) (Classic Reprint) - Rilegato
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Excerpt from A Contribution to the Theory of Linear Homogeneous Geometric Difference Equations (Q-Difference Equations)
In order to give a survey of the subject treated in this paper, I will here indicate the contents -of its particular sections. In 1 the main properties Of geometric factorial series are summarized. In 5 2 the proof of the existence of a system of solutions of the difference equation in question is given. In 3 these solutions are examined with regard to their asymptotic character and a proof of their linear independence is given. In 4 an examination of the analytic character Of the solutions is undertaken, and the solutions given by Grevy and Carmichael are de duced. In 5 some applications to particular equations are made. The list of literature p. 43 contains only works quoted in the paper. Of these I will especially mention the already cited works of Frobenius and nor lund, of which I have made frequent'use.
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