d-Z,(x) 1 dZ,(z) (1+)2=0 (E6) l,(z) 2x)=1K(z) (E7) eKv(z) 1,(2)=ewx2J,(el12),-<ag(s→ l,()=e/3v7/2J, (e-j3x/2). T 2s arg(z) (E10) K,(e)=ejv/H(ze/ 2), -T<arg-2 (E11) K(2)=-1c-m/H(e-1/),-x<amg(x)≤r (E12) (E13) Kn(x)=jn+HOAx) (E.14) d2n()+2dn(2)+ n(n+1) zn(z)=0.n=0,±1,±2 (E15) jn (z) Zn(z) jn()=5-Jn+,(2) (E17) bg(a)=√H()=hn()+m() (E.19) 2(a)=z(o)=h()-m1() n()=(-1)+1j-an+1)(x) (E21) Orthogonality relationships C4(2mn)4(m) 24+(pm)=am2[p ], @2001 by CRC Press LLCd2Z¯ ν (x) dz2 + 1 z d Z¯ ν (z) dz − 1 + ν2 z2 Z¯ ν = 0 (E.6) Z¯ ν (z) =  Iν (z) Kν (z) (E.7) L(z) =  Iν (z) e jνπ Kν (z) (E.8) Iν (z) = e− jνπ/2 Jν (ze jπ/2 ), −π < arg(z) ≤ π 2 (E.9) Iν (z) = e j3νπ/2 Jν (ze− j3π/2 ), π 2 < arg(z) ≤ π (E.10) Kν (z) = jπ 2 e jνπ/2H(1) ν (ze jπ/2 ), −π < arg(z) ≤ π 2 (E.11) Kν (z) = − jπ 2 e− jνπ/2H(2) ν (ze− jπ/2 ), −π 2 < arg(z) ≤ π (E.12) In(x) = j −n Jn(j x) (E.13) Kn(x) = π 2 j n+1H(1) n (j x) (E.14) d2zn(z) dz2 + 2 z dzn(z) dz + 1 − n(n + 1) z2 zn(z) = 0, n = 0, ±1, ±2,... (E.15) zn(z) =    jn(z) nn(z) h(1) n (z) h(2) n (z) (E.16) jn(z) =  π 2z Jn+ 1 2 (z) (E.17) nn(z) =  π 2z Nn+ 1 2 (z) (E.18) h(1) n (z) =  π 2z H(1) n+ 1 2 (z) = jn(z) + jnn(z) (E.19) h(2) n (z) =  π 2z H(2) n+ 1 2 (z) = jn(z) − jnn(z) (E.20) nn(z) = (−1) n+1 j−(n+1)(z) (E.21) Orthogonality relationships  a 0 Jν pνm a ρ  Jν pνn a ρ  ρ dρ = δmn a2 2 J 2 ν+1(pνn) = δmn a2 2  J ν (pνn) 2 , ν> −1 (E.22)