INFINITE SERIES 137 



6.802 Special Developments in Fourier's Series. 



f(x) = a from x = kc to x = (k + -)c, 



f(x) = -a from x = (k + -)c to x = (k + i)c, 

 where k is any integer, including o. 



oo 



,, x 40 '^ i . 2(2n-i)w 

 f(x) = / . sm x. 



J 7T SLJ 2H - I C 



n = i 



6.803 /(*) = mx, - - $ x $ + - 



4 4 



m(*-c), 



4 4 



5 ^ If 

 4 4 



- I)TT 



* 



m(x-c), +- < x < ^, 



r/ v Cm^\ -l"" 1 . 2H7TX 



f(x) = 7 . - - sm - 

 TT ^-^ n c 



n i 



/(x) - - a, - 5 & ^ x ^ - 



= a - (x + 26), - 3^ .r ^ - 



- 6 ^ a; ^ + b, 



8\/2a f TTA: i STTO: i JTTX i 



^1_- COS-: ^COS^-r- ; COS *-=- + -; COS 



7T 2 1 46 3 2 4^ 5 4^ 7 



