A power series in mathematics (in one variable) is an infinite series of a certain form. It normally appears as the Taylor series of a known function.
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There is no such thing as a "d meaning".
The meaning of mathematics trivia is to help someone learn math. Many people quiz their students on multiplication for example.
The Fourier series is a specific type of infinite mathematical series involving trigonometric functions that are used in applied mathematics. It makes use of the relationships of the sine and cosine functions.
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It has no special meaning.