function [E,number_of_terms]=Kepler(e,M)

%%Kepler.m will take in the values e and M in the expression M=E-esinE and
%%solve for E exactly by using an expansion in Bessel functions of the
%%first kind of order m

sum_of_bessels=0;           %initialize sum to zero
i=1;                        %index of summation set to 1
bessel_term(i)=(1/i)*besselj(i,i*e)*sin(i*M)

for i=1: 10
    bessel_term(i

%while abs(bessel_term(i)) > 0.1          %Term in expansion is negligible
 %   sum_of_bessels=sum_of_bessels+bessel_term(i);
  %  number_of_terms=i;
   % i=i+1;
   %end

%E=M+2*sum_of_bessels;