Difference between revisions of "T (n+1)(x)-2xT n(x)+T (n-1)(x)=0"
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(Created page with "==Theorem== The following formula holds for $n=0,1,2,\ldots$: $$T_{n+1}(x)-2xT_n(x)+T_{n-1}(x)=0.$$ ==Proof== ==References== Category:Theorem Category:Unproven") |
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==Theorem== | ==Theorem== | ||
The following formula holds for $n=0,1,2,\ldots$: | The following formula holds for $n=0,1,2,\ldots$: | ||
| − | $$T_{n+1}(x)-2xT_n(x)+T_{n-1}(x)=0 | + | $$T_{n+1}(x)-2xT_n(x)+T_{n-1}(x)=0,$$ |
| + | where $T_n$ denotes [[Chebyshev T|Chebyshev polynomials of the first kind]]. | ||
==Proof== | ==Proof== | ||
Latest revision as of 22:14, 19 December 2017
Theorem
The following formula holds for $n=0,1,2,\ldots$: $$T_{n+1}(x)-2xT_n(x)+T_{n-1}(x)=0,$$ where $T_n$ denotes Chebyshev polynomials of the first kind.
