136 MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



6.711 The complete elliptic integral of the second kind: 



If 



FOURIER'S SERIES 



6.800 If /(#) is uniformly convergent in the interval: 



-c<x< +c 



., x I. TTO: 27TX 



f(x) = -&o + &1 COS -- h 2 COS -- 1- & 3 COS 



2 C C C 



. TTX . 2TX 7.TTX 



+ a\ sm + #2 sm -- \- a s sin v2 + 

 c c c 



= -. r/(*) 



C J - c 



I (+< , . 



- / /(*) si 



C J - c 



mirx 



COS - 



-c C 



/-f- 

 J(x) sm 



c 



6.801 If f(x) is uniformly convergent in the interval: 



o<x<c 



j-/ \ i , z. , z. i. 



f(X) = - bo + 0i COS 1- 02 COS h 03 COS -f . . . . 



2 



. 2TTX . 47TX . 6lTX 



sin 1- <z 2 sin [- a 3 sin f- 



c c c 



2 C ., v 2W7T^ , 



= - I /(*) COS 0V 



C / o C 



