Difference between revisions of "Orthogonality relation for cosine on (0,pi)"
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(Created page with "==Theorem== The following formula holds for $m,n \in \{0,1,2,\ldots\}$ with $m\neq n$: $$\displaystyle\int_0^{\pi} \cos(mt)\cos(nt) \mathrm{d}t=0.$$ ==Proof== ==References==...") |
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==Theorem== | ==Theorem== | ||
The following formula holds for $m,n \in \{0,1,2,\ldots\}$ with $m\neq n$: | The following formula holds for $m,n \in \{0,1,2,\ldots\}$ with $m\neq n$: | ||
| − | $$\displaystyle\int_0^{\pi} \cos(mt)\cos(nt) \mathrm{d}t=0 | + | $$\displaystyle\int_0^{\pi} \cos(mt)\cos(nt) \mathrm{d}t=0,$$ |
| + | where $\cos$ denotes [[cosine]]. | ||
==Proof== | ==Proof== | ||
Revision as of 22:09, 19 December 2017
Theorem
The following formula holds for $m,n \in \{0,1,2,\ldots\}$ with $m\neq n$: $$\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) $(1.2)$
