J1.m

function res=J1(x)
% The MIT License (MIT)
%
% Copyright (c) 2022 Roman Szewczyk
%
% Permission is hereby granted, free of charge, to any person obtaining a copy
% of this software and associated documentation files (the "Software"), to deal
% in the Software without restriction, including without limitation the rights
% to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
% copies of the Software, and to permit persons to whom the Software is
% furnished to do so, subject to the following conditions:
% 
% The above copyright notice and this permission notice shall be included in all
% copies or substantial portions of the Software.
% 
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
% IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
% FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
% AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
% LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
% OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
% SOFTWARE.
% 
%
% DESCRIPTION:
% Function calculating Bessel functions of the first kind, 1 order 
% connected with the paper:
% A. Ostaszewska-Lizewska, D. Kopala, R. Szewczyk
% "Improved control of mesh density in adaptive tetrahedral meshes 
% for finite element modeling"
% submitted to Measurement Automation Robotics Journal
% (Pomiary Automatyka Robotyka), www.par.pl
%
 fun1 = @(t) exp(i.*(t-x.*sin(t)));
 res =  1./(2.*pi).*quadgk(fun1,-1.*pi,pi,180);
 
end