Your result can be proved very easily by using a result given in Brychkov, Prudnikov, Marichev, Integral and Series, Vol.3, p-91, $ 7.3.7.3 by taking a = b = 1.
For more results of this type, send an e-mail to me for my research paper.
All the vry best,
Arjun K. Rathie,
India