Plot Bessel function first kind of order and second kind of order

 Plot Bessel function of first kind of order and second kind of order

                   Bessel functions , first defined by the mathematician Daniel  Bernouli and generalized by Friedrich Bessel.  More on wikipedia.

In python,to plot Bessel function of first kind of order and second kind of order or more , there is an inbuilt library in scipy , with the scipy modules special function we can plot the graph for visualization . 

See the Scipy document resources.

Method:

• Import numpy module for array creation .
• Import matplotlib for plotting the graph .
• Import scipy special module .
• Using numpy linspace for liearly space array . 

Source code :

import numpy as np  
 import matplotlib.pyplot as plt  
 from scipy.special import jv , yn  
 newparams = {'axes.labelsize': 10, 'axes.linewidth': 1.5, 'savefig.dpi':   
    1000,   
    'lines.linewidth': 2, 'figure.figsize': (12, 10),    
    'legend.frameon': True,   
    'legend.handlelength': 0.7}   
 plt.rcParams.update(newparams)   
 x= np.linspace(0,10,1000)  
 plt.subplot(1,2,1)  
 col = ['r','b','g','y']  
 for i in range(4):   
   J = jv(i,x)  
   plt.plot(x,J,c=col[i] ,label='$J_%d(x)$'%i ,markevery =None)   
 plt.legend(loc = 'best' ,prop={'size':12})   
 plt.xlabel('x')   
 plt.ylabel(r' $( J_n(x)$)')  
 plt.ylim(-1,1)  
 plt.axhline(0 , color='black')  
 plt.title("Bessel function of the first kind of order")  
 plt.grid()  
 plt.subplot(1,2,2)  
 col = ['r','b','g','y']  
 for i in range(4):   
   K = yn(i,x)  
   plt.plot(x,K,c=col[i] ,label='$Y_%d(x)$'%i ,markevery =None)   
 plt.legend(loc = 'best' ,prop={'size':12})   
 plt.xlabel('x')   
 plt.ylabel(r' $( Y_n(x)$)')  
 plt.axhline(0 , color='black')  
 plt.title("Bessel function of the second kind of order")  
 plt.ylim(-1,1)  
 plt.grid()  
 """###### Sub plot Adjusting ######"""  
 plt.subplots_adjust(left=0.1,  
           bottom=0.1,   
           right=0.9,   
           top=0.9,   
           wspace=0.4,   
           hspace=0.4)  
 plt.suptitle('Graphical Representation of Bessel Function',fontsize=18,color='b',fontstyle ="italic")   
 plt.show()