Bessho 



G* can be integrated as (1,15) 



''* CD 



G* (C0S5) = 2^ X^n ^2n ^e2n(^--q) • ^^^^ 



n = 



The minimum solution is a solution such that 



G(y) = constant , (42) 



but, putting this into Eq. (31) results in a differential equation, so that 



G*(y) = constant (43) 



may be a special solution, but there is also a homogeneous solution: 



G*(y) = C cosh (gy/vT) , (44) 



where C is an arbitrary constant, for which 



G(y) =0 and r* = . (45) 



This solution will be called a wave-free solution (1). 

 Since there are expansions (15) 



1= 2^(-l)nA:^"^ ce,„(^.-q), (46) 



n = 



cosh (g cos 0/v^) = J^ (-1)" Cj^ ce2„(^,-q) , (4?) 



n = 



where 



2(-l)" Ao'"^ Ce2„(sinh-i 1,-q) 

 *^'" " ce2„(0,q) • 



the general solution can be written in the form 



H(y) = aH^Cy) - bHb(y) . a-b=l. (48) 



where 



00 



Ha(y) = 0a(^)/sin ■ 0a(^) = 21 ^2n ^e^^C^.-q) , (^9) 



784 



