FUNCTION : printtype2 - print a Type 2 identity
CALLING SEQUENCE : printtype2(L, eqn, num)
PARAMETERS : L - list [p,a,c1,N,B]
eqn, num - positive integers
GLOBAL VARIABLES : _F
SYNOPSIS :
Prints identity for
G(a)*G(p) + c1*H(a)*H(p)
with equation number (eqn.num)
EXAMPLES :
> with(qseries):
> with(thetaids):
> with(ramarobinsids):
> G:=j->1/GetaL([1],10,j):H:=j->1/GetaL([3],10,j):
> GM:=j->1/MGetaL([1],10,j): HM:=j->1/MGetaL([3],10,j):
> GE:=j->-GetaLEXP([1],10,j):HE:=j->-GetaLEXP([3],10,j):
> proveit:=true: xprint:=false:
> findtype2(6);
*** There were NO errors. Each term was modular function on
Gamma1(60). Also -mintotord=40. To prove the identity
we need to check up to O(q^(42)).
To be on the safe side we check up to O(q^(160)).
*** The identity below is PROVED!
[2, 3, -1]
3
eta(15 tau) eta(12 tau) eta(10 tau) eta(4 tau)
_G(2) _G(3) - _H(2) _H(3) = -----------------------------------------------
2 2
eta(30 tau) eta(20 tau) eta(5 tau) eta(2 tau)
[[2, 3, -1]]
> L:=PROVEDFL2[1];
L := [2, 3, -1, 60, -40]
> printtype2(L,3, 2);
3
eta(15 tau) eta(12 tau) eta(10 tau) eta(4 tau)
G(2) G(3) - H(2) H(3) = -----------------------------------------------,
2 2
eta(30 tau) eta(20 tau) eta(5 tau) eta(2 tau)
Gamma[1](60), -B = 40, (3.2)
DISCUSSION :
SEE ALSO :
findtype2,
printtype1, printtype2, printtype3, printtype4,
printtype5, printtype6, printtype7, printtype8,
printtype9, printtype10, printtypelist