#bessel functions

Introduction Bessel functions, named after Friedrich Bessel, are canonical solutions to Bessel’s differential equation: $x^2y” + xy’ + (x^2 – n^2)y = 0$ This equation arises in many physical problems, including heat conduction, vibrations of circular membranes, and quantum mechanics. Bessel Functions of the First Kind The Bessel function of the first kind $J_n(x)$ is defined by the…

A series of Bessel Functions of the First Kind: https://en.wikipedia.org/wiki/Bessel_function

MATLAB SCRIPT:

y = linspace (-10,100, 1000);

[x0] = besselj(0, y); [x1] = besselj(1, y); [x2] = besselj(2, y); [x3] = besselj(3, y); [x4] = besselj(4, y); [x5] = besselj(5, y); [x6] = besselj(6, y); [x7] = besselj(7, y); [x8] = besselj(8, y); [x9] = besselj(9, y); [x10] = besselj(10, y); [x11] = besselj(11, y);

plot (y, x0, 'LineWidth', 1.5, 'Color',[0.4,0,0]) %red hold on plot (y, x1, 'LineWidth', 1.5, 'Color',[0.4,0.4,0])%yellow plot (y, x2, 'LineWidth', 1.5, 'Color',[0,0.4,0])%green plot (y, x3, 'LineWidth', 1.5, 'Color',[0,0,0.4])%blue plot (y, x4, 'LineWidth', 1.5, 'Color',[0.8,0,0])%red plot (y, x5, 'LineWidth', 1.5, 'Color',[0.8,0.8,0])%yellow plot (y, x6, 'LineWidth', 1.5, 'Color',[0,0.8,0])%green plot (y, x7, 'LineWidth', 1.5, 'Color',[0,0,0.8])%blue plot (y, x8, 'LineWidth', 1.5, 'Color',[1,0,0])%red plot (y, x9, 'LineWidth', 1.5, 'Color',[1,1,0])%yellow plot (y, x10, 'LineWidth', 1.5, 'Color',[0,1,0])%green plot (y, x11, 'LineWidth', 1.5, 'Color',[0,0,1])%blue