We have to prove:
Now, we consider the LHS.
Now, we make the substitution:
Therefore, we get:
Now by Maclaurin series,
This can also be written as:
On plugging the value into LHS, we get:
Now, by Ramanujan's Master Theorem, we get
Therefore, by Euler's Reflection Formula, we get
Now, we consider RHS as:
On differentiating both the sides wrt a, we get:
Now we make the substitution:
Therefore, we get
On evaluating this integral as above, we get
Since we can directly integrate the above expression wrt a.
Therefore we get:
Hence we can conclude that .