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You can get an approximate answer by doing a series expansion of the integrand. As always, the more terms used in the expansion, the better the approximation. expr = Exp[(Γ^2 (Cos[ϕ]^2 Sin[θ]^2 σx^2 + Sin[ϕ]^2 Sin[θ]^2 σy^2) - 2 c Γ (x0 Cos[ϕ] Sin[θ] + y0 Sin[ϕ] Sin[θ]))/(2 c^2)]; f[n_Integer, ϕ0_] := Integrate[Series[expr, {ϕ, ...

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