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
axis([-10 100 -0.58 1]) legend('J_0', 'J_1', 'J_2', 'J_3', 'J_4', 'J_5', 'J_6', 'J_7', 'J_8', 'J_9', 'J_{10}', 'J_{11}', 'Location', 'northeast') xlabel('x'); ylabel('y(x)'); title({'Bessel Functions of the First Kind'});