Prove that

**Solution**

**Lemma 1: **Let . It holds that

**Lemma 2: **Let . It holds that

We begin by squaring the identity of lemma 2. Hence,

Integrating the last equation we get,

Expanding the LHS we get that

Finally,

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Prove that

**Solution**

**Lemma 1: **Let . It holds that

**Lemma 2: **Let . It holds that

We begin by squaring the identity of lemma 2. Hence,

Integrating the last equation we get,

Expanding the LHS we get that

Finally,

Generally speaking,

(1)

Proof:The function is analytic in the open disk . Using Gauss Mean Value Theorem we have that:Since it follows that

Using the above formula we can also extract the following result