The following function is defined over the interval [-L, L]: f(x) = px4 + qx5. If it is expressed as a Fourier series, f(x) = a_{0} + \sum ↙\stackrel{\infty}{n = 1} \{a_{n} \sin ⁡ (\frac{\pi x}{L}) + b_{n}\cos ⁡ (\frac{\pi x}{L}) \}, which options amongst the following are true?

an, n = 1, 2, ..., ∞ depend on p

an, n = 1, 2, ..., ∞ depend on q

bn, n = 1, 2, ..., ∞ depend on p

bn, n = 1, 2, ..., ∞ depend on q

GATE Civil Engineering (CE) 2023 Shift 1 Solved Paper

Question : 25 of 65

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The following function is defined over the interval [-L, L]:
f(x) = px4 + qx5.
If it is expressed as a Fourier series,

f(x) = a_{0} + ∑ ↙{n = 1}↖{∞} \{a_{n} sin \;⁡ (\;{π\;x}/{L}) + b_{n}\cos ⁡ (\;{π\;x}/{L}) \}

,
which options amongst the following are true?

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