In order to find a root of a polynomial equation
(1)
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consider the difference equation
(2)
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which is known to have solution
(3)
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where , , ..., are arbitrary functions of with period 1, and , ..., are roots of (1). In order to find the absolutely greatest root (1), take any arbitrary values for , , ..., . By repeated application of (2), calculate in succession the values , , , .... Then the ratio of two successive members of this sequence tends in general to a limit, which is the absolutely greatest root of (1).