#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 el,m,L,R,z,omega:


el:=sqrt(m*t):
z:=exp(s/el):
omega:=exp(2*Pi*I/el):


L:= (  ((omega^v*z)^(1/2) +  (omega^v*z)^(-1/2)))^(2*m):
R:= el*binomial(2*m,m+el*v)*z^(el*v):

simplify(asympt(L, m, 1)), simplify(asympt(R,m,1));


end: