INFINITE SERIES 



6.707 sin 



Example i. f(x) = e~ kx [>>o]. 



CO 



i e kir + e~ kir 



2k 



4 



n = i 



Replacing k by -, and subtracting, 



Example 2. With /(#) = g-^* cos ju^ and e"^ sin /uc. 



00 r ^ 



X " I X X Trsinh 2X?r 



' X 2 + M 2 ^ ( X 2 + ( - M ) 2 X 2 + ( + M ) 2 J COSh 2X7T - COS 2M7T 



> 



n - JJL n + fj, \ Trsin 2/z?r 



' X 2 + M 2 ^ X 2 + (n - ju) 2 X 2 + ( + M) 2 I cosh 2\7r - cos 2//7T 



w i ^ 



6.709 If the sum of the series, 



is known, then 



/00 



if g < / y ~ l f(f) dt 

 a + aiy + a*y(y + i) + fl?y(y + i) (y + 2) + ..... =Jo _ 



6.710. The complete elliptic integral of the first kind: 



/ d* /-r rf9 



J oV(i- x 2 ) (i - * 2 r 2 ) Jo Vi - 2 si 



If 



i + 

 K = 1 ^- 



T . 3 \ ^ 



2^4/ V ' * J 



2-4-6 



