Hot answers tagged calculus-and-analysis
11
It is Kampé de Fériet function, introduced in Joseph Kampé de Fériet, "La fonction hypergéométrique.", Mémorial des sciences mathématiques, Paris, Gauthier-Villars.
Its definition is given on Notations page:
and, in an alternative form, in Wikipedia:
$${}^{p+q}f_{r+s}\left(
\begin{matrix}
a_1,\cdots,a_p\colon b_1,b_1{}';\cdots;b_q,b_q{}'; \\
...
5
Hopefully we're converging on the desired integral:
Assuming[(0 < x1 < x2 < 1),
Integrate[n (n - 1) (1 - y)^(n - 2), {y, 0, x2}, {x, 0, x1}]]
which has answer
(n x1 (-1 + (1 - x2)^n + x2))/(-1 + x2)
Though it may be that what you are after is:
Assuming[(0 < x1 < x2 < 1),
Integrate[n (n - 1) (1 - y)^(n - 2), {x, 0, x1}, {y, 0, ...
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