content_image/409516.jpg content_image/409517.jpg content_image/409523.jpg content_image/409524.jpg content_image/409525.jpg content_image/409526.jpg content_image/409527.jpg content_image/409528.jpg content_image/409529.jpg
function as given in equation (9.9.1) from [48] 

<img src='content_image/409516.jpg'>

Using the above relation, the asymptotic limit to the BipoSH coefficients turn out to be 

<img src='content_image/409517.jpg'>

Appendix B: Generalized evolution equation for statistical isotropy breakdown 

Starting with equation (29), putting P$_{ℓ}$ ( ˆ k · ˆ n ) = 4 π 2 ℓ +1 ∑ m Y ∗ $_{ℓm}$( ˆ k ) Y$_{ℓm}$ (ˆ n ) and evaluating the double integral using the equation 

<img src='content_image/409523.jpg'>

the most general evolution equation becomes 

<img src='content_image/409524.jpg'>

where 

<img src='content_image/409525.jpg'>

Using the summation formula for four Clebsch-Gordon coefficients given by equation (9.1.8) from [48], 

<img src='content_image/409526.jpg'>

equation (B2) simplifies to 

<img src='content_image/409527.jpg'>

Substituting the multipole dependent coefficients as 

<img src='content_image/409528.jpg'>

the generalized evolution equation for deviations of statistical isotropy in the CMB brightness fluctuation reduces to 

<img src='content_image/409529.jpg'>

