Notes for AKT-090922/0:08:20: Difference between revisions

From Drorbn
Jump to navigationJump to search
No edit summary
 
No edit summary
 
(One intermediate revision by the same user not shown)
Line 1: Line 1:
For our theorem from last time about coefficients <math>j_n</math> of power series expansion of <math>J(e^x)</math> being knot invariants of type <math>n</math>, in fact we may replace <math>e^x</math> with any power series having the last two terms <math>x+1</math>.
'''Theorem''' (from last time) If we expand <math>J(K)(e^x)=\sum{J_n(K)x^n}</math> then <math>J_n</math> is an invariant of type <math>n</math>.

In fact, this holds if we substitute <math>e^x</math> by any power series that starts with <math>1+x</math> (e.g. <math>1+x</math>, <math>1+sinx</math>).

Latest revision as of 10:15, 14 September 2011

Theorem (from last time) If we expand then is an invariant of type .

In fact, this holds if we substitute by any power series that starts with (e.g. , ).