- Prove that
where as .
- Using part (a) prove
- Proof. We start with the algebraic identity
Replacing by we have,
By the definition of we have
Therefore,
Hence,
- Proof. First, we use the expansion of ,
where . By part (a) we then have as ,
Next, since we multiply this expansion for by the expansion (page 287 of Apostol) for as ,