Difference between revisions of "Orthogonality relation for cosine on (0,pi)"
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==References== | ==References== | ||
| − | * {{BookReference|An Introduction to Orthogonal Polynomials|1978|T.S. Chihara|prev=2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t)|next= | + | * {{BookReference|An Introduction to Orthogonal Polynomials|1978|T.S. Chihara|prev=2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t)|next=Orthogonality of Chebyshev T on (-1,1)}} $(1.2)$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 22:52, 19 December 2017
Theorem
The following formula holds for $m,n \in \{0,1,2,\ldots\}$ with $m\neq n$: $$\displaystyle\int_0^{\pi} \cos(mt)\cos(nt) \mathrm{d}t=0,$$ where $\cos$ denotes cosine.
Proof
References
- 1978: T.S. Chihara: An Introduction to Orthogonal Polynomials ... (previous) ... (next) $(1.2)$
