Those "cookbook coefficients" are correct, but you have to normalize to the PD biquad~ equation. This involves accounting for the a0 coefficient (folded into the other coefficients in the PD biquad~), and perhaps changing the sign of the aN coefficients (which affect they y, or previous-output, components), (depends on whether your equation specifies those coefficients as being added or subtracted, I can't remember at the moment).

Look up Julius Smith's (jos) book on digital filters - there is enough information in there about the math to translate. (I sent email on the same topic to the list earlier this week with the link)

I made a patch which uses the RBJ cookbook to calculate LPF coefficients for biquad~ in MSP, which is below. Don't have the time right now to make a PD version, but cyclone should mostly load it.

Jer

max v2; #N vpatcher 323 114 914 557; #P outlet 184 378 15 0; #P outlet 119 378 15 0; #P outlet 91 378 15 0; #P outlet 63 378 15 0; #P outlet 17 378 15 0; #P window setfont "Sans Serif" 9.; #P newex 184 274 63 196617 /~ 1.; #P newex 119 274 33 196617 /~ 1.; #P newex 63 274 33 196617 /~ 1.; #P newex 63 240 35 196617 !-~ 1.; #P newex 17 305 40 196617 *~ 0.5; #P newex 184 218 35 196617 !-~ 1.; #P newex 237 218 33 196617 +~ 1.; #P newex 119 240 39 196617 *~ -2.; #P newex 119 136 35 196617 cosx~; #P newex 184 166 289 196617 *~; #P newex 463 140 75 196617 expr sinh($f1); #P inlet 515 54 15 0; #P newex 463 118 30 196617 !/ 1.; #P newex 463 96 27 196617 * 2.; #P message 463 75 21 196617 $1; #P newex 463 53 45 196617 loadbang; #P newex 184 136 34 196617 sinx~; #P newex 279 62 53 196617 dspstate~; #P newex 184 106 119 196617 /~ 1.; #P newex 184 83 34 196617 *~ 2.; #P newex 184 61 70 196617 *~ 3.141593; #P inlet 184 36 15 0; #P comment 305 109 139 196617 frequency in radians (omega); #P comment 490 76 15 196617 Q; #P comment 16 398 18 196617 b0; #P comment 63 399 16 196617 b1; #P comment 91 399 17 196617 b2; #P comment 119 400 17 196617 a1; #P comment 185 399 19 196617 a2; #P comment 276 220 102 196617 a0 (common divisor); #P window setfont "Sans Serif" 14.; #P comment 333 303 163 196622 signal-rate biquad LPF coefficient calculator; #P fasten 28 0 26 0 68 296 22 296; #P connect 26 0 31 0; #P fasten 22 0 27 0 124 172 68 172; #P connect 27 0 28 0; #P connect 28 0 32 0; #P fasten 24 0 28 1 242 263 91 263; #P connect 26 0 33 0; #P fasten 12 0 22 0 189 130 124 130; #P connect 22 0 23 0; #P connect 23 0 29 0; #P connect 29 0 34 0; #P fasten 24 0 29 1 242 263 147 263; #P connect 9 0 10 0; #P connect 10 0 11 0; #P connect 11 0 12 0; #P connect 12 0 14 0; #P connect 14 0 21 0; #P connect 21 0 25 0; #P connect 25 0 30 0; #P connect 30 0 35 0; #P fasten 21 0 24 0 189 198 242 198; #P connect 24 0 30 1; #P connect 13 1 12 1; #P connect 15 0 16 0; #P connect 16 0 17 0; #P fasten 19 0 17 0 520 94 468 94; #P connect 17 0 18 0; #P connect 18 0 20 0; #P connect 20 0 21 1; #P pop;