“…If we define a n pk; tq " p´aq´n t βn pγnq k Γpα k`βn`1q pωt α q k k! " p´aq´n Γpγn`kq Γpγnq Γpα k`βn`1q 15) and recalling the asymptotic behaviour of the rate of gamma functions (see [8; 10]) Γ pz`aq Γ pz`bq " z a´b , for |z| Ñ 8, |Argpzq| ď π´ , |Argpz`aq| ď π´ , 0 ă ă π, it is easy to see thaťˇˇˇa n`1 pk; tq a n pk; tqˇˇˇˇ"ˇˇˇˇt β β a 1 nˇˇˇˇ, n Ñ 8 , @t ą 0, @k P N Y t0u , (2.16) hence lim nÑ8ˇa n`1 pk; tq a n pk; tqˇˇˇˇ" 0 , @t ą 0, @k P N Y t0u , (2.17) that concludes our proof of the absolute convergence of (2.12).…”