130 



LAMBERT— SOLUTION OF ALGEBRAIC EQUATIONS [April 25, 



the expressions at the right of the row in which the sign of inequahty 

 stands. 



29. The following table exhibits one set of conditions sufficient 

 for the absolute convergence of the infinite series which give the 

 roots of the four-term equation 



ay^ -\- by'' -}- cy'' -\- 1^=0 



together with the equations from which these series are obtained 

 and the number of roots given by each series, and also the conditions 

 sufficient for the absolute convergence of the series of corrections 

 which must be applied to the roots of this four-term equation to 

 obtain the roots of the five-term equation 



ay'^ + by'' -\- cy^ -\- dy^ -|- / = o. 



