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JinkuiZhao

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k := 1;
R := 1;
alpha := 1;
H := 1;
w[0] := 1;
eq[m] := A[m]*(HankelH1(m-1, k*R)-HankelH1(m+1, k*R))+sum(A[n](-exp(-(1/2)*i(m+n)*pi)*HankelH1(-m-n, 2*k*H)*BesselJ(1-m, k*R)+exp(-(1/2)*i(m+n)*pi)*HankelH1(-m-n, 2*k*H)*BesselJ(-1-m, k*R)), n = -2 .. 2)
= -i^m*w[0]*(BesselJ(m-1, k*R)-BesselJ(m+1, k*R))*(exp(-i*H*k*sin(alpha)-i*m*alpha)+exp(i*H*k*sin(alpha)+i*m*alpha));
eq[m1] := subs(m = 1, eq[m]);
eq[m2] := subs(m = 2, eq[m]);
eq[m0] := subs(m = 0, eq[m]);
eq[m-1] := subs(m = -1, eq[m]);
eq[m-2] := subs(m = -2, eq[m]);
solve({eq[m-2], eq[m-1], eq[m0], eq[m1], eq[m2]}, {A[-2], A[-1], A[0], A[1], A[2]});
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