Unformatted text preview: , . . . . (5) Show the formula (2). (b) Apply (a) to ﬁnd the Fourier series of the 2periodic functions f 1 ( x ) = 1x , f 2 ( x ) = x 2 , (1 ≤ x < 1). 2. Prove the following formulas: ( a ) ∞ X k =1 (1) k 2 k1 = π 4 ( b ) ∞ X 1 n 2 = π 2 6 Hint : Use the Fourier series expansions of the 2 πperiodic functions f ( x ) = 1 ifπ ≤ x < 1 if 0 ≤ x < π , respectively g ( x ) = x 2 ....
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 Fall '08
 FriedmannBrock
 Differential Equations, Equations, Partial Differential Equations, Fourier Series, 1L, Riemann, 2L, 4 k, 1 2K

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