没怎么看明白你的问题, 我觉得
list = {{a1, b1}, {a2, b2}, {a3, b3}};
newlist =
Transpose@{First@Transpose[list],
FoldList[Plus, Last@Transpose[list]]};
f = Interpolation[Join[{{0, 0}}, newlist]]
newlist是{{a1, b1}, {a2, b1+b2}, {a3, b1+b2+b3}}, 再使用Interpolation得到插值函数f
