This preview shows page 1. Sign up to view the full content.
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 ....
View
Full
Document
This note was uploaded on 02/07/2011 for the course MATH 212 taught by Professor Friedmannbrock during the Fall '08 term at American University of Beirut.
 Fall '08
 FriedmannBrock
 Differential Equations, Equations, Partial Differential Equations, Fourier Series

Click to edit the document details