10. For , > 0, show that B(, ) = 2 E 0 t 21 (1 + t 2 ) (+) dt. Hint:

10. For α, β > 0, show that B(α, β) = 2 E ∞ 0 t 2α−1 (1 + t 2 ) −(α+β) dt. Hint: Make the substitution x = t 2/(1 + t 2) in B(α, β) = E 1 0 xα−1 (1 − x)β−1 dx.