1481 
The problem is further simplified by replacing the 
term peop fw with the Dirichlet discontinuous factor 
expressed in the form 
ee —|,w<o 
=| -/ i 
cake ore x exp(cwx)de =}o0 wero 
ta = P G ye PL j , (13) 
tee — 06 +l, woo 
The symbol aE stands for "principal value." Equation (12) 
then becomes 
co 2) 
“¢, ' 
Fle) - (27) ™ P a | plu) exp LE wlerx)/ A® a4) 
-oo a) 
and the problem reduces to the evaluation of the double integral 
F (t) for specific cases in which (w) is aveilable. 
In the case of an exponentially decaying shock wave 
oO 7 ce (2) 
? 
2At 
P. Cian: } (715) 
Al) 
tT2O 
i (16) 
Cer)” (Ar eu) 
ple 
Substitution of (16) into (14) and evaluation of the complex 
integral in © by standard methods of contour integration 
