content_image/327104.jpg content_image/327105.jpg content_image/327103.jpg content_image/327102.jpg content_image/327101.jpg content_image/327099.jpg content_image/327100.jpg
where ¯ a$_{p}$ = ( 1 − √ c$_{p}$ ) 2 and ¯ b$_{p}$ = ( 1 + √ c$_{p}$ ) $^{2}$. Further, let 

<img src='content_image/327104.jpg'>

<img src='content_image/327105.jpg'>

Finally, for any permutation ρ of the sequence (1 , 2 , ..., r ) and any vector z = ( z$_{1}$, ..., z$_{r}$ ), let 

<img src='content_image/327103.jpg'>

where S = λ$_{1}$ + ... + λ$_{p}$. 

Proposition 2 Let the contour K that encircles λ$_{1}$, ..., λ$_{p}$ counter-clockwise be chosen so that for any z ∈ K , Re z < ( ∑ r j =1 h$_{j}$ 1+ h$_{j}$ ) − 1 S . Then 

<img src='content_image/327102.jpg'>

<img src='content_image/327101.jpg'>

where i denotes the imaginary unit, the summation in (19) is over all permutations ρ of the sequence (1 , 2 , ..., r ) , 

<img src='content_image/327099.jpg'>

<img src='content_image/327100.jpg'>

In the next section, we perform the asymptotic analysis of L ( h ; λ ) and L ( h ; µ ) that relies on the Laplace approximations of the contour integrals in (18) and (19) after the contours are suitably deformed without changing the value of the inte- grals. 

