content_image/310723.jpg content_image/310724.jpg content_image/310728.jpg
<img src='content_image/310723.jpg'>

We next evaluate the second component denoted C$_{2}$ directly as follows, 

<img src='content_image/310724.jpg'>

Finally, to evaluate the third component denoted C$_{3}$ we use the substitution z = αp$_{α}$$_{+}$ − v $^{∗}$/α and integrate-by-parts as done in C$_{1}$ . We suppress the details for brevity and present the final expression. 

<img src='content_image/310728.jpg'>

Note that Φ ( b ∗ α ) − Φ ( a ∗ α ) = − Φ ( − b ∗ α ) + Φ ( − a ∗ α ) and hence the relevant term from equa- tion (A.12) and equation (A.14) can be collected together when adding the expressions. 

