FUNCTION : qseries[sift] - Pick out the terms of a q-series in which the exponent belongs to a fixed residue class mod p CALLING SEQUENCE : sift(s,q,n,k,T) PARAMETERS : f - q-series T - positive integers SYNOPSIS : Suppose s is the q-series s = sum a[i] q^i O(q^T) then sift(s,q,n,k,T) returns the q-series sum a[n*i+k] q^i T EXAMPLES : > s:=series(etaq(q,1,500)^3,q,500); 3 6 10 15 21 28 36 45 s := 1 - 3 q + 5 q - 7 q + 9 q - 11 q + 13 q - 15 q + 17 q - 19 q 55 66 78 91 105 120 136 153 + 21 q - 23 q + 25 q - 27 q + 29 q - 31 q + 33 q - 35 q 171 190 210 231 253 276 300 + 37 q - 39 q + 41 q - 43 q + 45 q - 47 q + 49 q 325 351 378 406 435 465 496 - 51 q + 53 q - 55 q + 57 q - 59 q + 61 q - 63 q 500 + O(q ) ----------------------------------------------------------------------------- > sift(s,q,7,6,500); 7 21 42 70 - 7 + 21 q - 35 q + 49 q - 63 q ----------------------------------------------------------------------------- > series(%+7*etaq(q,7,70)^3,q,71); 77 O(q ) ----------------------------------------------------------------------------- > SEE ALSO :