PRACTICAL APPLICATION OF THE FOURIER INTEGRAL 675 

 TABLE I (Continued) 



air 



L4. 



15. 



16. 



Coefficient F(f) for the 

 Cisoidal Oscillation 



sin ap 



sin ^p 



sin ap 



cos ^p 



17. 



cos ap 



a sin Pp 1 



18. 



19.* 

 20. 



i21. 



122. 



123. 



^p sin ap p 



cos Pp 1 



^ cos ap p 



cosh.{ap) 

 cosh(ap) 1 



P P 



cosh(ap) 



R{^) < R(a) 



i?(/3) < Ria) 



Coefficient G(g) for the 

 Unit Impulse 



4a2 cosh2 Jl 

 2a 



1 . xi3 

 — sin — 

 2a a 



cosh — ^ + cos — 



1 '^^ ^^.t. '"^ 

 - cos — cosn -— 



a 2a 2a 



cosh — ^ + cos — 



i?(/3) < R{a) 



i?(/3) < i?(a) 



tanh^ 1 

 a , za _ 1 



— tan-i t^t: 



7r)3 ^ 7r/3 2 



ctn-- 

 2a 



0<±g 



cos- 



x/3 



tan-i 



IT 



sinh 



TTg 



1 



{p — po)cosh{apo) p — po 

 sinh.{ap) 



sinh.{ap) _ I 

 P 



ap^ 



|[^o(g + a) + ^o(g - a)-] 



=Fi, 0<±g<a 



i cis(27r/og)[tanh(fl/>o) =F 1], 



< ± £ < a 



2a 



^h 



— a < g < a 

 < ± g < a 



* A star marks a pair as being the limit approached by regular pairs. 



