How to find out the source of a mathematical formula published on:
?
I mean the representation of the Euler beta function by series with an increasing factorial. I need this to place in the list of references.
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.
Unfortunately, the link from Wikipedia leads just to Beta function : Series representations (formula 06.18.06.0007)
but the question is where (from which journal article) this result is taken. I have to refer to the original source. (No doubts about the truth of the formula).
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.
Thank you and everyone, I found this formula in a slightly modified form in:
Bateman, Erdélyi. Higher transcendental functions. Vol. 1, section 1.4, formula (2).
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 think it would be good manners on the part of the management to keep somewhere a list of the primary sources of all the information that is contained on the site.