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Splitting the domain of integration into segments [ p − α √ p, p − αp γ ] , [ p − αp $^{γ}$, p + αp $^{γ}$] and [ p + αp $^{γ}$, p + α √ p ] , where 0 < γ < 1 / 2 , and denoting the corresponding inte- grals by I $^{(1)}$, I(2) and I $^{(3)}$, respectively, we have 

<img src='content_image/323260.jpg'>

<img src='content_image/323261.jpg'>

<img src='content_image/323262.jpg'>

Using the Laplace approximation, we have 

so that I (2) dominates I (1) and I (3) and 

This implies that 

<img src='content_image/323263.jpg'>

<img src='content_image/323264.jpg'>

<img src='content_image/323265.jpg'>

<img src='content_image/323266.jpg'>

and hence, only constant and linear terms in the expansion of ˜ θ$_{pj}$ ˜ v$_{pj}$ − 1 2 p ∑ p i $_{=1}$ln ( 1+2 ˜ θ$_{pj}$ ˜ v$_{pj}$ − 2 ˜ θ$_{pj}$λ$_{pi}$ ) into power series of x p − 1 matter for the evaluation of I (0 , ∞ ) . Let us find these terms. 

