Max does suggest a different order of the coefficients in its help file, but what we see in practice is yet some other order, and also some reversal in signs (positive/negative) in a couple of terms.
Just wondering, why the hell is that? Anybody?
Can't deal with formulas really well, but I see they're supposed to be the same... and I take that from mmb's patches, whose formulas are exactly as depicted in max (although the help from native pd's biquad~ is somewhat different, but seemingly equivalent mathematically)
ps. by the way, here's a patch that converts the order of coefficients from "max to pd"
#N canvas 150 47 214 262 10;
#X obj 32 7 unpack f f f f f;
#X obj 125 31 * -1;
#X obj 101 55 * -1;
#X obj 41 80 pack f f f f f;
#X msg 41 115 \$4 \$5 \$3 \$2 \$1;
#X obj 32 -23 inlet;
#X obj 41 143 outlet;
#X text 69 -24 max;
#X text 87 143 pd;
#X connect 0 0 3 0;
#X connect 0 1 3 1;
#X connect 0 2 3 2;
#X connect 0 3 2 0;
#X connect 0 4 1 0;
#X connect 1 0 3 4;
#X connect 2 0 3 3;
#X connect 3 0 4 0;
#X connect 4 0 6 0;
#X connect 5 0 0 0;