Nowaekt and Sharma 
with 
F(3)(n,q) = q if fe dkp Ge sal ae (B24) 
0 
The integrals pl) and (3) can be solved in closed form [ see 
formulas 2.6334 and 2.3212 in Gradshteyn and Ryzhik (1965) ] or 
evaluated by recurrence formulas : 
F() (0,p) = 0, 
F() (m,p) = 2m { (2m-1) [ sin(p)-F((m -1,p)] /p-cos (p)}/p 
F(3)(0,q) = 1-exp(-q) , 
FG)(n,q) = -exp(-q) + nF@G)(n-1,q) /q (B25) 
Similarly , the free-wave spectrum of the propeller can be written as 
l+v 
Gp(u)+iF p(u) = Eyl dR frao fo (R,8) exp {s°(zp#R sin 9) 
+ i(sx Xp + uR cos0)) | (B26) 
If the propeller source distribution o is a function of radius only , 
then this simplifies by virtue of transverse symmetry to 
l+v 
Gy (u)+iF (u) = oe v exp( 5? Zz p'is*,) fe )dR yi exp(s¢R sin@)x 
cos (uR cos @)d@ 
l+v Ne 
= 1674 { = exp ( s2zptisxp) rf Ro(R)I,5(sR)dR 
Ry (B27) 
1892 
