#C26.txt; April 23, 2018 #Having Maple do Polya's combintorial proof of the modularity of the theta function Help:=proc(): print(`Polya(s,t,v)`): end: Polya:=proc(s,t,v) local l,m,L,R,z,omega: l:=sqrt(m*t): z:=exp(s/l): omega:=exp(2*Pi*I/l): L:= ( ( ((omega^v*z)^(1/2) + (omega^v*z)^(-1/2)))/2)^(2*m): R:= l*binomial(2*m,m+l*v)*z^(l*v)/2^(2*m): factor(limit(L, m=infinity)), simplify(limit(R,m=infinity)); end: