FUNCTION : printtype5 - print a Type 5 identity
CALLING SEQUENCE : printtype5(L, eqn, num)
PARAMETERS : L - list [a,p,c1,N,B]
num,eqn - 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],12,j): H:=j->1/GetaL([5],12,j):
> GM:=j->1/MGetaL([1],12,j): HM:=j->1/MGetaL([5],12,j):
> GE:=j->-GetaLEXP([1],12,j): HE:=j->-GetaLEXP([5],12,j):
> proveit:=true: xprint:=false:
> findtype5(6);
*** There were NO errors. Each term was modular function on
Gamma1(48). Also -mintotord=24. To prove the identity
we need to check up to O(q^(26)).
To be on the safe side we check up to O(q^(120)).
*** The identity below is PROVED!
[1, 2, -1]
eta(16 tau) eta(6 tau) eta(tau)
_GM(1) _GM(2) - _HM(1) _HM(2) = ----------------------------------
eta(48 tau) eta(12 tau) eta(2 tau)
[[1, 2, -1]]
> L:=PROVEDFL5[1];
L := [1, 2, -1, 48, -24]
> printtype5(L,3, 5);
eta(16 tau) eta(6 tau) eta(tau)
G*(1) G*(2) - H*(1) H*(2) = ----------------------------------, Gamma[1](48),
eta(48 tau) eta(12 tau) eta(2 tau)
-B = 24, (3.5)
DISCUSSION :
SEE ALSO :
findtype1,
printtype1, printtype2, printtype3, printtype4,
printtype5, printtype6, printtype7, printtype8,
printtype9, printtype10, printtypelist/a>