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    Metadata details:
    filename: sum2.m
    path of file: ./repos/chebfun/@ballfun
    
    the code of the file until where you have to start completion: function ff = sum2(f, dims)
% SUM2 Definite integration of a BALLFUN in two variables.
%   SUM2(F, DIMS) integrates F over two of the variables r, lambda or theta 
%   where DIMS is a row vector containing two of the three indices
%   1, 2 or 3. The output is a 1D CHEBFUN in the remaining variable.
%
%   G = SUM2(F) is the same as SUM2(F, [2, 3]).
%
% See also SUM, SUM3. 

% Copyright 2019 by The University of Oxford and The Chebfun Developers.
% See http://www.chebfun.org/ for Chebfun information.

% Empty check
if ( isempty(f) )
    ff = chebfun();
    return
end


% Default to lambda and theta 
    
function of r after the multiplication by r^2
    % (measure)
    ff = chebfun(A, 'coeffs');
    
elseif dim_1 == 1 &&  dim_2 == 2
    % Integrate over r and lambda
    
    % Multiplication by r^2 in Chebyshev basis
    Mr2 = ultraS.multmat(m, [.5;0;.5], 0 );
    F = reshape(Mr2*reshape(F, m, []),m, n, p);
    
    % Coefficients of integration between 0 and 1 of the chebyshev polynomials
    IntChebyshev = zeros(1,m);
    for i = 0:m-1
        if mod(i,4)==0
            IntChebyshev(i+1) = -1/(i^2-1);
        elseif mod(i,4)==1
            IntChebyshev(i+1) = 1/(i+1);
        elseif mod(i,4)==2
            IntChebyshev(i+1) = -1/(i^2-1);
        else
            IntChebyshev(i+1) = -1/(i-1);
        end