INVERSE METHOD OF DEFINITE INTEGRALS. 367 



in sines Fn = 2 sin (p {sin {n + l)(p — . sin {n + 3)(p 



+ ^^ -^ . sm (« + 5) <^ - &c. ] 



37. The Junction F„ is transient. 



Either of the preceding values of F„ give F„ = Fn—F", where 



F: = cos {n(t>) - ^±i . cos {n + 2).(p + ^^"^^^^^^^ • ^^^ (« + 4) <^ + &c. 

 F„"= cos (w + 2) <^ - ^^ . cos (« + 4) . <^ + {n + l){n + 2) ^^^ („ ^ g^ ^ ^ ^^. 

 passing from trigonometrical to exponential values, 



1 1.2' 



1 1.2" 



_ ("g.^vrr ^ g-</>vrT\-" 

 = 2cos«0, 



2F„" = £("+2)*^^ - ""'"^ . e("+4)*v^ + (" + l)(^ + 2) _ ^(„^g)^^— _ ^^ 



1 1.2 



+ g-(n + 2),^V:rT _ ^jt2,e-(n + 4)0V^ ^ (w + 1) (W + 2) ^-(„ + 4)^vri _ j^^.^ 



= 2 COS «^, 

 hence F„=-F';-F„"=0. 



