Talk:Hudde's rules

Latest comment: 6 years ago by SebastianHelm in topic Rule 1 and the "modern theorem"

Rule 1 and the "modern theorem"

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The definition of the polynomial   numbers the coefficients just opposite to the way we define it at Polynomial#Definition and anywhere else throughout Wikipedia, which makes summation and derivation more cumbersome. Instead, I would just go with the common definition and write (if the expanded form with dots is even necessary):

 

and similarly

 

This then lends itself, since the   form an arithmetic progression, to the simplification

 
 
 

Thus showing the connection to the "modern theorem". But what's the name of the "modern theorem"; is it covered anywhere? (Maybe in its generalized form for any multiple roots.) ◄ Sebastian 21:05, 12 April 2018 (UTC)Reply