In the Wikipedia article on Borel summation, there is the following quote attributed to Gösta Mittag-Leffler:
Borel, then an unknown young man, discovered that his summation method gave the 'right' answer for many classical divergent series. He decided to make a pilgrimage to Stockholm to see Mittag-Leffler, who was the recognized lord of complex analysis. Mittag-Leffler listened politely to what Borel had to say and then, placing his hand upon the complete works by Weierstrass, his teacher, he said in Latin, 'The Master forbids it'.
I am interested in learning more about the context of this quote; why would Weierstrass have forbidden this technique? The article also states:
There are several variations of this method that are also called Borel summation, and a generalization of it called Mittag-Leffler summation.
So despite his initial objections, I guess Mittag-Leffler came around to the idea eventually?