FUNCTION :  printtype3 -  print a Type 3 identity
                

CALLING SEQUENCE :  printtype3(L, eqn, num)                  

PARAMETERS :  L - list [a1,p1,c2,a2,p2,c2,N,B]
            num,eqn - positive integers

GLOBAL VARIABLES : _F

SYNOPSIS :   
   Prints  identity for
    (G(a1)*G(p1) + c1 *H(a1)*H(p1))
    /(G(a2)*H(p2)+c2*H(a2)*G(p2)):
   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:
>  findtype3(6);
*** There were NO errors.  Each term was modular function on
    Gamma1(60). Also -mintotord=64. To prove the identity
    we need to  check up to O(q^(66)).
    To be on the safe side we check up to O(q^(184)).
*** The identity below is PROVED!
[2, 3, -1, 6, 1, -1]
                                        2            2            5
 _G(2) _G(3) - _H(2) _H(3)   eta(60 tau)  eta(15 tau)  eta(10 tau)  eta(6 tau)
 ------------------------- = -------------------------------------------------
 _G(6) _H(1) - _H(6) _G(1)              5            2           2
                             eta(30 tau)  eta(20 tau)  eta(5 tau)  eta(2 tau)

                             [[2, 3, -1, 6, 1, -1]]

>  L:=PROVEDFL3[1];
                       L := [2, 3, -1, 6, 1, -1, 60, -64]

>  printtype3(L,3, 2);
                                   2            2            5
G(2) G(3) - H(2) H(3)   eta(60 tau)  eta(15 tau)  eta(10 tau)  eta(6 tau)
--------------------- = -------------------------------------------------,
G(6) H(1) - H(6) G(1)              5            2           2
                        eta(30 tau)  eta(20 tau)  eta(5 tau)  eta(2 tau)

    Gamma[1](60), -B = 64,     (3.2)



DISCUSSION :

SEE ALSO :  

findtype3,
printtype1, printtype2, printtype3, printtype4,
printtype5, printtype6, printtype7, printtype8,
printtype9, printtype10, printtypelist