77 
1914-15.] Integral-Equations and Lame’s Functions. 
into which Mathieu’s differential equation transforms when fj. is put zero, 
that is, the equation 
^ + nhj = 0, 
as- 
so 
y{s) = cos ns. 
Equation (12) thus becomes 
Jo 
- iC cos s 7 
e cos ns as 
which will be recognised as one form of the trigonometrical integral for the 
Bessel functions. 
{Issued separately March 16, 1915.) 
