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
CHANGES :
1.3: o sift can now handle negative powers of q.
For the old-version use oldsift.
EXAMPLES :
> with(qseries):
> 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 )
-----------------------------------------------------------------------------
> Y:=etaq(q,1,1000)/etaq(q,25,1000)/q:
> S:=series(Y^5,q,1000):
> etamake(S,q,100);
5
eta(tau)
------------
5
eta(25 tau)
> S0:=sift(S,q,5,0,900):
> etamake(S0,q,20);
6
eta(tau)
-----------
6
eta(5 tau)
SEE ALSO :