Category:Half-Range Fourier Series
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This category contains results about Half-Range Fourier Series.
Definitions specific to this category can be found in Definitions/Half-Range Fourier Series.
Half-Range Fourier Cosine Series
Let $\map f x$ be a real function defined on the interval $\openint 0 \lambda$.
Then the half-range Fourier cosine series of $\map f x$ over $\openint 0 \lambda$ is the series:
- $\map f x \sim \dfrac {a_0} 2 + \ds \sum_{n \mathop = 1}^\infty a_n \cos \frac {n \pi x} \lambda$
where for all $n \in \Z_{\ge 0}$:
- $a_n = \ds \frac 2 \lambda \int_0^\lambda \map f x \cos \frac {n \pi x} \lambda \rd x$
Half-Range Fourier Sine Series
Let $\map f x$ be a real function defined on the interval $\openint 0 \lambda$.
Then the half-range Fourier sine series of $\map f x$ over $\openint 0 \lambda$ is the series:
- $\map f x \sim \ds \sum_{n \mathop = 1}^\infty b_n \sin \frac {n \pi x} \lambda$
where for all $n \in \Z_{> 0}$:
- $b_n = \ds \frac 2 \lambda \int_0^\lambda \map f x \sin \frac {n \pi x} \lambda \rd x$
Subcategories
This category has only the following subcategory.
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Pages in category "Half-Range Fourier Series"
The following 4 pages are in this category, out of 4 total.