## ABSTRACT

L1(x) µ−1L2(x)ν−1L3(x)λ−1 dx

where Lj are linear functions and L1(a) = L2(b) = 0. For example, 3.198 (5.4.2)∫ 1 0

xµ−1(1− x)ν−1 [ax+ b(1− x) + c]−(µ+ν) dx = (a+ c)−µ(b+ c)−νB(µ, ν)

is reduced to the normal form (5.2.3) by writing

(5.4.3) I = (b + c)−µ−ν ∫ 1 0

xµ−1(1 − x)ν−1(1− rx)−(µ+ν) dx

with r = (b− a)/(b+ c). Then (5.2.3) gives

(5.4.4) I = (b + c)−µ−νB(µ, ν)2F1

( µ+ ν, µ; µ+ ν;

b− a

) .