Using the orthogonality properties of the Clebsch-Gordan coefficients and the spherical harmonics, we obtain the well-known one-dimensional angle independent integral equation $$ T_{ll'}^{\alpha}(kk'K\omega)=V_{ll'}^{\alpha}(kk') +\frac{2}{\pi}\sum_{l''}\int_{0}^{\infty} dqq^2 \frac{V_{ll''}^{\alpha}(kq) T_{l''l'}^{\alpha}(qk'K\omega)} {\omega -H_0}. $$ Inserting the denominator we arrive at $$ \hat{T}_{ll'}^{\alpha}(kk'K)=\hat{V}_{ll'}^{\alpha}(kk') +\frac{2}{\pi}\sum_{l''}\int_{0}^{\infty} dqq^2 \hat{V}_{ll''}^{\alpha}(kq) \frac{1}{k^2-q^2 +i\epsilon} \hat{T}_{l''l'}^{\alpha}(qk'K). $$