请问为什么Mathematica中对同一个函数级数展开的一次项的系数和求偏导后取相同x0得到的值会不同In[907]:= ClearAll[ff, r, M, A, B, c, ddc, ddA, \[Alpha], rm, g, z, \r0, h, p, q, a, b, br, bd, d, um, R, hh, RR1, RR, rr1, rr, fff]M = 1/2;ff[r_] = 1 - 1/r + \[Alpha]/r^2;A[r_] = ff[r];B[r_] = 1/ff[r];c[r_] = r^2;ddc[r_] = D[c[r], {r, 2}];ddA[r_] = D[A[r], {r, 2}];dA[r_] = D[A[r], {r, 1}];rm = Solve[D[c[r], {r, 1}]/c[r] == D[A[r], {r, 1}]/A[r], r][[2, 1, 2]]; // Simplifyrm = 3/4 (1 + Sqrt[1 - 32 /9 \[Alpha]]);r = (r0^2 + Sqrt[ r0^4 - 4 r0^2 \[Alpha] (r0 - r0 z - \[Alpha] + z \[Alpha])])/( 2 (r0 - r0 z - \[Alpha] + z \[Alpha]));R[z_, r0_] = (2 Sqrt[A[r] B[r] c[r0]])/(c[r] dA[r]) (1 - A[r0]);hh[z_, r0_] = 1/Sqrt[ 1 - 1/r0 + \[Alpha]/r0^2 - 1/r^2*((r0 - \[Alpha])*z + (r0^2 - r0 + \[Alpha]))];um = Sqrt[c[rm]/A[rm]];h[z_, r0_] = 1/Sqrt[p[r0, z]*z + q[r0, z]*z^2];p[r0_, z_] = (r0 - \[Alpha])/( r0 - 2*\[Alpha])*(2 - 3/r0 + (4 \[Alpha])/r0^2);q[r0_, z_] = ( r0*(r0 - \[Alpha])^2)/(r0 - 2*\[Alpha])^3*(3/r0 - 1 - (9 \[Alpha])/ r0^2 + (8 \[Alpha]^2)/r0^3);q[rm, 0]; // Simplifyg[z_, rm_] = R[z, rm] hh[z, rm] - R[0, rm] 1/Sqrt[p[rm, 0] z + q[rm, 0] z^2];(*Series[R[0,rm]1/Sqrt[p[rm,0]z+q[rm,0]z^2],{\[Alpha],0,1}]*)SeriesCoefficient[g[z, rm], {\[Alpha], 0, 1}]RR[z_] = D[g[z, rm], \[Alpha]] /. \[Alpha] -> 0 // SimplifyClearAll[ff, r, M, A, B, c, \[Alpha], rm, z, r0, h, p, q, a, b, br, \bd, d, um, R, hh, RR1, RR, rr1, rr, fff]Out[927]= -(8/(9 Sqrt[z^2])) - (8 (3 - 7 z + 3 z^2))/( 3 Sqrt[3] (-3 + 2 z) Sqrt[-z^2 (-3 + 2 z)])Out[928]= (8 Sqrt[ z^2] (3 Sqrt[3] Sqrt[z^2] - 7 Sqrt[3] z Sqrt[z^2] + 3 Sqrt[3] (z^2)^(3/2) - 3 Sqrt[-z^2 (-3 + 2 z)] + 2 z Sqrt[-z^2 (-3 + 2 z)]))/(9 (-z^2 (-3 + 2 z))^(3/2))

ClearAll[ff, r, M, A, B, c, ddc, ddA, \[Alpha], rm, g, z, \
r0, h, p, q, a, b, br, bd, d, um, R, hh, RR1, RR, rr1, rr, fff]
M = 1/2;
ff[r_] = 1 - 1/r + \[Alpha]/r^2;
A[r_] = ff[r];
B[r_] = 1/ff[r];
c[r_] = r^2;
ddc[r_] = D[c[r], {r, 2}];
ddA[r_] = D[A[r], {r, 2}];
dA[r_] = D[A[r], {r, 1}];
rm = Solve[D[c[r], {r, 1}]/c[r] == D[A[r], {r, 1}]/A[r], r][[2, 1,
2]]; // Simplify
rm = 3/4 (1 + Sqrt[1 - 32 /9 \[Alpha]]);
r = (r0^2 + Sqrt[
r0^4 - 4 r0^2 \[Alpha] (r0 - r0 z - \[Alpha] + z \[Alpha])])/(
2 (r0 - r0 z - \[Alpha] + z \[Alpha]));
R[z_, r0_] = (2 Sqrt[A[r] B[r] c[r0]])/(c[r] dA[r]) (1 - A[r0]);
hh[z_, r0_] = 1/Sqrt[
1 - 1/r0 + \[Alpha]/r0^2 -
1/r^2*((r0 - \[Alpha])*z + (r0^2 - r0 + \[Alpha]))];
um = Sqrt[c[rm]/A[rm]];
h[z_, r0_] = 1/Sqrt[p[r0, z]*z + q[r0, z]*z^2];
p[r0_, z_] = (r0 - \[Alpha])/(
r0 - 2*\[Alpha])*(2 - 3/r0 + (4 \[Alpha])/r0^2);
q[r0_, z_] = (
r0*(r0 - \[Alpha])^2)/(r0 - 2*\[Alpha])^3*(3/r0 - 1 - (9 \[Alpha])/
r0^2 + (8 \[Alpha]^2)/r0^3);
q[rm, 0]; // Simplify
g[z_, rm_] =
R[z, rm] hh[z, rm] - R[0, rm] 1/Sqrt[p[rm, 0] z + q[rm, 0] z^2];
(*Series[R[0,rm]1/Sqrt[p[rm,0]z+q[rm,0]z^2],{\[Alpha],0,1}]*)
SeriesCoefficient[g[z, rm], {\[Alpha], 0, 1}]
RR[z_] = D[g[z, rm], \[Alpha]] /. \[Alpha] -> 0 // Simplify
ClearAll[ff, r, M, A, B, c, \[Alpha], rm, z, r0, h, p, q, a, b, br, \
bd, d, um, R, hh, RR1, RR, rr1, rr, fff]
Out[927]= -(8/(9 Sqrt[z^2])) - (8 (3 - 7 z + 3 z^2))/(
3 Sqrt[3] (-3 + 2 z) Sqrt[-z^2 (-3 + 2 z)])
Out[928]= (8 Sqrt[
z^2] (3 Sqrt[3] Sqrt[z^2] - 7 Sqrt[3] z Sqrt[z^2] +
3 Sqrt[3] (z^2)^(3/2) - 3 Sqrt[-z^2 (-3 + 2 z)] +
2 z Sqrt[-z^2 (-3 + 2 z)]))/(9 (-z^2 (-3 + 2 z))^(3/2))

等价的，化简结果不同罢了。