content_image/312420.jpg content_image/312419.jpg content_image/312418.jpg content_image/312417.jpg content_image/312416.jpg
Using these results, it is easy to show that 

<img src='content_image/312420.jpg'>

Using (B.1) and (B.8), it can be shown that 

The Beta function is defined in terms of the Gamma function as 

Integral representations of the Beta function are 

<img src='content_image/312419.jpg'>

<img src='content_image/312418.jpg'>

<img src='content_image/312417.jpg'>

## B.2 Hypergeometric Functions 

The generalized hypergeometric function is defined as 

<img src='content_image/312416.jpg'>

where the constants a$_{i}$ , b$_{i}$ are called indices and uniquely define each generalized hypergeo- metric function. From this definition it is clear that the ordering of the indices is irrelevant and that if any a$_{i}$ = b$_{j}$ (1 ≤ i ≤ p , 1 ≤ j ≤ q ), the generalized hypergeometric function $_{p}$F$_{q}$ reduces to p − $_{1}$F$_{q}$$_{−}$$_{1}$ . When p = q + 1, the generalized hypergeometric function has a branch cut on the interval z ∈ [1 , ∞ ). Generalized hypergeometric functions can also be 

