The Fourier Series of a Function $f$ Defined On $[ - p , p ]$

question 19

Multiple Choice

The Fourier Series of a function $f$ defined on $[ - p , p ]$ is $f ( x ) = a _ { 0 } / 2 + \sum _ { n - 1 } ^ { \infty } \left( a _ { n } \cos ( n \pi x / p ) + b _ { n } \sin ( n \pi x / p ) \right)$ where Select all that apply.

• A) \(a _ { 0 } = \int _ { -p } ^ { p } f ( x ) d x / p\)
• B) \(a _ { n } = \int _ { -p} ^ { p } f ( x ) \cos ( n \pi x / p ) d x / p\)
• C) \(a _ { n } = \int _ { - p } ^ { p } f ( x ) \sin ( n \pi x / p ) d x / p\)
• D) \(b _ { n } = \int _ { - p } ^ { p } f ( x ) \cos ( n \pi x / p ) d x / p\)
• E) \(b _ { n } = \int _ { - p } ^ { p } f ( x ) \sin ( n \pi x / p ) d x / p\)

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Definitions:

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