✓, ) = 1 X n=0 n X m= n ˇ Bm n hn(kr)Y m n (✓, ) <latexit sha1_base64="CGN8lKd9T9sqiB0gRW/T9PgOq6Y=">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</latexit> ˇ Bm n + 2⇡jk Q X q=1 ˚ Dm,qjn(krq)P|m| n (0) = 0 <latexit sha1_base64="TiKjBu+6sjWVr0l4xLtD9UbCnQY=">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</latexit> ˚ D even m = 1 2⇡jk ⇣ UT |m| U|m| ⌘ 1 UT |m| ˇ Beven m <latexit sha1_base64="YKPL9ethyxwVPaHP8G5o8gGuD6I=">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</latexit> ɿ७ڏ S1(r, ✓, ) = Q X q=1 Z 2⇡ 0 D(rq, 0) G(r, rq)| ✓0=0 d 0 = 1 X n=0 n X m= n 2⇡jk Q X q=1 ˚ Dm,q P|m| n (0)jn(krq)hn(kr)Y m n (✓, ) <latexit sha1_base64="RiA0IsyMkowjM0T44I31QDvJk/Y=">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</latexit> ɿ௨ৗෳૉ S(r, ✓, ) = 1 X n=0 jn(kr0)hn(kr)Y 0 n (0, 0)Y 0 n (✓, ) + 1 X n=0 jn(kr0)hn(kr)Y 0 n (⇡, 0)Y 0 n (✓, ) <latexit sha1_base64="m5O+41KEOffqI2choIC45P9Owlg=">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</latexit> = jk 1 X n=0 r (2n + 1) ⇡ jn(kr0)hn(kr)Y 0 n (✓, ) <latexit sha1_base64="fJkVP9NrJMnBW0kkXS0WLTHWjBE=">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</latexit> ˇ Beven 0 = jk p ⇡ h j0(kr0), p 5j2(kr0), · · · , p 2N + 1jN (kr0) iT <latexit sha1_base64="kRUUCMdFEnBvNZokpmYSLDAL3uA=">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</latexit> ˚ D even 0 = D = 1 2⇡jk ⇣ UT 0 U0 ⌘ 1 UT 0 ˇ Beven 0 <latexit sha1_base64="wfbBqaLZMiZLzg4gqhTfbR6x6aQ=">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</latexit> z <latexit sha1_base64="2nAWqti7tIwnqDQtKHSZtxGcVsA=">AAACZHichVFNSwJBGH7cvswsLQmCICQxOskYQh8noUtHP/IDTGR3G21x3V12V0GlP1DXokOngojoZ3TpD3TwDwTR0aBLh17XhSip3mFmnnnmfd55ZkYyVMWyGet5hLHxickp77Rvxj87FwjOL+QtvWnKPCfrqm4WJdHiqqLxnK3YKi8aJhcbksoLUn13sF9ocdNSdG3fbhu83BBrmlJVZNEmKt2pBCMsxpwIj4K4CyJwI6UHb3GAQ+iQ0UQDHBpswipEWNRKiIPBIK6MLnEmIcXZ5ziGj7RNyuKUIRJbp7FGq5LLarQe1LQctUynqNRNUoYRZU/sjvXZI7tnL+zj11pdp8bAS5tmaajlRiVwspR9/1fVoNnG0ZfqT882qthyvCrk3XCYwS3kob7VuehndzLR7hq7Zq/k/4r12APdQGu9yTdpnrmEjz4g/vO5R0F+IxZPxLbTiUgy6X6FF8tYxTq99yaS2EMKOTqX4xRnOPc8C34hJCwOUwWPqwnhWwgrn/2SigQ=</latexit> ±r0 <latexit sha1_base64="+iofLvTkUcmiNY4B+ZX25jt7MXk=">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</latexit>