You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: simpleWingSetRollRateRed.m
    path of file: ./repos/LADAC/aerodynamics/simple_wing
    
    the code of the file until where you have to start completion: function wing = simpleWingSetRollRateRed( wing )
% simpleWingSetRollRateRed computes a factor (0~1) that compensates the
% roll damping for a wing that has no infinite aspect ratio.

    
function wing = simpleWingSetRollRateRed( wing )
% simpleWingSetRollRateRed computes a factor (0~1) that compensates the
% roll damping for a wing that has no infinite aspect ratio.
% 
% Literature:
%   [1] Schlichting, H. & Truckenbrodt, E. (2001): Aerodynamik des
%       Flugzeuges - Teil 2, Springer.
% 

% Disclamer:
%   SPDX-License-Identifier: GPL-3.0-only
% 
%   Copyright (C) 2020-2022 Yannic Beyer
%   Copyright (C) 2022 TU Braunschweig, Institute of Flight Guidance
% *************************************************************************

lambda = wing.geometry.b/wing.geometry.c;

c_L_d_Omega_x = rollDamping( lambda, 2*pi );

lambda_inf = 1000;
c_L_d_Omega_x_inf = rollDamping( lambda_inf, 2*pi );

wing.roll_rate_red_factor = c_L_d_Omega_x / c_L_d_Omega_x_inf;


    % [1], eq. (7.207)
    function c_L_d_Omega_x = rollDamping( Lamdbda, c_L_alpha_inf )
        k = pi*Lamdbda/c_L_alpha_inf;
        c_L_d_Omega_x = -0.25*pi*Lamdbda/(sqrt(k^2+4)+2);
    end