The functions U and F for the following formula (alpha-representation of Feynman integrals)

can be generated by the simple Mathematica code:

UF[xx_, yy_, z_] := Module[{degree, coeff, i, t2, t1, t0, zz},
    zz = Map[Rationalize[##,0]&, z, {0, Infinity}];
    degree = -Sum[yy[[i]]*x[i], {i, 1, Length[yy]}];
    coeff = 1;
    For[i = 1, i <= Length[xx], i++,
        t2 = Coefficient[degree, xx[[i]], 2];
        t1 = Coefficient[degree, xx[[i]], 1];
        t0 = Coefficient[degree, xx[[i]], 0];
        coeff = coeff*t2;
        degree = Together[t0 - ((t1^2)/(4 t2))];
    ];
    degree = Together[-coeff*degree] //. zz;
    coeff = Together[coeff] //. zz;
    {coeff, Expand[degree], Length[xx]}
]

where xx is the set of loop momenta, yy is the set of propagators and z is the set of replacements.

For example, for the same 2-loop tadpole with 2 massive lines and 1 massless line one can genarate U and F by

UF[{v, q}, {v^2 - mm, q^2 - mm, (v - q)^2}, {mm -> 1}]