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