FUNCTION : printtype7 - print a Type 7 identity
CALLING SEQUENCE : printtype7(L, EQNNAME, num, nL)
PARAMETERS : L - list [a,p,c1,N,B]
num - positive integer (no. of identity found by findtype7)
nL - number of identities
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:
> findtype7(6);
*** There were NO errors. Each term was modular function on
Gamma1(24). Also -mintotord=4. To prove the identity
we need to check up to O(q^(6)).
To be on the safe side we check up to O(q^(52)).
*** The identity below is PROVED!
[1, 1, -1]
4
eta(12 tau) eta(8 tau)
_GM(1) _G(1) - _HM(1) _H(1) = ----------------------------------
3
eta(24 tau) eta(6 tau) eta(4 tau)
*** There were NO errors. Each term was modular function on
Gamma1(24). Also -mintotord=4. To prove the identity
we need to check up to O(q^(6)).
To be on the safe side we check up to O(q^(52)).
*** The identity below is PROVED!
[1, 1, 1]
4
eta(6 tau) eta(4 tau)
_GM(1) _G(1) + _HM(1) _H(1) = ----------------------------------------------
2
eta(24 tau) eta(12 tau) eta(8 tau) eta(2 tau)
[[1, 1, -1], [1, 1, 1]]
> L:=PROVEDFL7[1];
L := [1, 1, -1, 24, -4]
> printtype7(L,3, 5);
4
eta(12 tau) eta(8 tau)
G*(1) G(1) - H*(1) H(1) = ----------------------------------, Gamma[1](24),
3
eta(24 tau) eta(6 tau) eta(4 tau)
-B = 4, (3.5)
DISCUSSION :
SEE ALSO :
findtype7,
printtype1, printtype2, printtype3, printtype4,
printtype5, printtype6, printtype7, printtype8,
printtype9, printtype10, printtypelist