The Fourier Coeficients of the Function $f ( x ) = x ^ { 2 }$

question 12

Multiple Choice

The Fourier coeficients of the function $f ( x ) = x ^ { 2 }$ on $[ - 1,1 ]$ are Select all that apply.

• A) \(a _ { 0 } = 2 / 3\)
• B) \(a _ { n } = 0\)
• C) \(a _ { n } = 4 ( - 1 ) ^ { n } / \left( n ^ { 2 } \pi ^ { 2 } \right)\)
• D) \(b _ { n } = 0\)
• E) \(b _ { n } = 4 ( - 1 ) ^ { n } / \left( n ^ { 2 } \pi ^ { 2 } \right)\)

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Definitions:

Stock Dividends

These are dividends paid by a company to its shareholders in the form of additional shares of stock, rather than in cash.

Contributed Capital

Funds raised by a company through the issuance of shares to investors, representing the stockholders' equity apart from retained earnings.

Retained Earnings

The portion of net income left over for a business after it has paid out dividends to its shareholders, often used for reinvestment in the business or to pay down debt.

Small Stock Dividend

A dividend payment made in the form of additional shares, typically less than 25% of the existing shares.