Скачать или смотреть Part 2: Plot Besselj Jv(x) of the 1st, and bessely Yv(x) 2nd kind and derivative for integer v=0

Thanks for watching:

besselj (alpha,x) ( J_V (x) ) or J = besselj(nu,Z) ( J_V (z) ) - Compute Bessel of the 1st kind.
bessely(alpha,x) (Y_V (x) ) or Y=bessely(nu,Z) ( Y_V (z) ) - Compute Bessel of the 2nd kind.
besseli (alpha,x) ( I_V (x) )or I =besseli(nu,Z) ( I_V (x) ) - Modified Bessel of the 1st kind.
besselk(alpha,x) ( K_V (x) )or K =besselk(nu,Z) (K_V (z) )- Modified Bessel of the 2nd kind.

Plot of Bessel function of the first, second kind and modified for,Jv(x) for integer v = 0. −J1(x) is the derivative of J0(x) much like −sin x is the derivative of cos x

Applications of Bessel functions
Finding separable solutions to Laplace's equation
Bessel functions are important for many problems of wave propagation and static potentials.

Link for more knowledge: https://mpmath.org/doc/current/functi...

Coding:
% special functions - bessel fuctions
x = linspace(0,10,100); %define array
%plot different bessel graphs and derivatives
%compute bessel function of the 1st kind and derivative
subplot(2,2,1), plot(x, besselj(0,x), x,-besselj(1,x)), legend('J_0','-J_1'), title('besselj and derivative'), xlabel('x'), ylabel('J_\nu(x)'), grid on
%compute bessel function of the 2nd kind and derivative
subplot(2,2,2), plot(x, bessely(0,x), x,-bessely(1,x)), legend('Y_0','-Y_1'), title('bessely and derivative'), xlabel('x'), ylabel('Y_\nu(x)'), grid on
%compute modified bessel function of the 1st kind and derivative
subplot(2,2,3), plot(x, besseli(0,x), x,-besseli(1,x)), legend('I_0','-I_1'), title('besseli and derivative'), xlabel('x'), ylabel('I_\nu(x)'), grid on
%compute modified bessel function of the 2nd kind and derivative
subplot(2,2,4), plot(x, besselk(0,x), x,-besselk(1,x)), legend('K_0','-K_1'), title('besselk and derivative'), xlabel('x'), ylabel('K_\nu(x)'), grid on

Thank you
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Part 1: Bessel Functions - Plot Besselj Jv(x) of the 1st kind, and bessely Yv(x) 2nd kind and modified for integer v=0 -    • Part 1: Plot Besselj Jv(x)of the 1st kind ...  
Part 2 Bessel functions - Plot Besselj Jv(x) of the 1st kind, and bessely Yv(x) 2nd kind and derivative for integer v=0 -    • Part 2: Plot Besselj Jv(x) of the 1st, and...  
Part 3 Besel functions: Plot Besselj Jv(x) of the 1st kind, and bessely Yv(x) 2nd kind for integer orders v=1,2,3 -    • Part 3: Plot Besselj Jv(x) of the 1st kind...  

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