Nowaekt and Sharma 
n i+j Gm e) 2-0) ay 
oe agit = 
‘ Tr Pe Py ) i ay = 4 i, 
i=0 j= 
where 
ai ins i 3 
Ej (bab + ) = dé as é ‘i 3/2 
ig kl ge ee 
E+] on ti ee } 
(B39) 
This double integral E;,; has a closed form solution (for constant 
limits of integration) amenable to numerical evaluation by a recurrence 
formula . (The authors are indebted to Drs K. Eggers and H. Kajitani 
for this suggestion ) . Consider the indefinite integral 
(B40) 
By repeated use of formula 2.2631 from Gradshteyn and Ryzhik 
( 1965 ) it can be shown that 
1 . : 
4 fh—S> whol : jtl Fa 
Bij Lit) ee Ey, )-()( F201 +y Fs, ;)f 
1 eet i+] 2 
(B41) 
Hence, starting from the four fundamental solutions 
EQ 0 = ve arctan (yr/xz) 
Eg = - In (x+r) 
Ei o = - ln (ztr) 
Pe oe (B42) 
1896 
