Nikolay, thanks for the info! I myself looked in Abramowitz and Stegun: "Handbook of Mathematical Functions ..." and even in Encyclopædia Britannica (I own one of the last printed editions!), but in vain.

I'll explain: I've derived a similar but somewhat different formula for the case Re a > 0, Re b < 0. Publication requires a comparison and indication of the author of the alternative formula.

I need this to place in the list of references. ...

This is more like a question: Is a citation here really necessary? I mean, it appears to be a mathematical fact - you can directly evaluate:

Sum[Pochhammer[1 - b, k]/((a + k) k!), {k, 0, Infinity}]

to get

$$ \frac{\Gamma(1+a) \cdot \Gamma(b)}{a \cdot \Gamma(a+b)} $$

and from this it is evident that we see here the Euler beta function.

But if you really need a citation - here is one from Wikipedia.