mathematica吧 关注：19,647贴子：73,432
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我认为这个积分暂时无法得出结果的原因是, 按照先积x再积y, 或者先积y再积x是积不出来的, 但你可以这样做
eq = Assuming[r >= 0,
FullSimplify@
TransformedField["Cartesian" -> "Polar",
E^(-I*(m*x + n*y))*(x + y)*
E^(-Sqrt[x^2 + y^2]), {x, y} -> {r, \[Theta]}]];
FullSimplify@
Integrate[
Assuming[{\[Theta] >= 0, (m | n) \[Element] Reals},
Integrate[r*eq, {r, 0, Infinity}]], {\[Theta], 0, 2 Pi}]
eq = Assuming[r >= 0,
FullSimplify@
TransformedField["Cartesian" -> "Polar",
E^(-I*(m*x + n*y))*(x + y)*
E^(-Sqrt[x^2 + y^2]), {x, y} -> {r, \[Theta]}]];
FullSimplify@
Integrate[
Assuming[{\[Theta] >= 0, (m | n) \[Element] Reals},
Integrate[r*eq, {r, 0, Infinity}]], {\[Theta], 0, 2 Pi}]
