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Bessel function of second kind


Y = bessely(nu,Z)
Y = bessely(nu,Z,1)


The differential equation


A solution Yν(z) of the second kind can be expressed as


and Γ(a) is the gamma function. Yν(z) is linearly independent of Jν(z).

Jν(z) can be computed using besselj.


Y = bessely(nu,Z) computes Bessel functions of the second kind, Yν(z), for each element of the array Z. The order nu need not be an integer, but must be real. The argument Z can be complex. The result is real where Z is positive.


Y = bessely(nu,Z,1) computes bessely(nu,Z).*exp(-abs(imag(Z))).


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Vector of Function Values

Create a column vector of domain values.

z = (0:0.2:1)';

Calculate the function values using bessely with nu = 1.

format long
ans =


Plot Bessel Functions of Second Kind

Define the domain.

X = 0:0.1:20;

Calculate the first five Bessel functions of the second kind.

Y = zeros(5,201);
for i=0:4
    Y(i+1,:) = bessely(i,X);

Plot the results.

axis([-0.1 20.2 -2 0.6])
grid on;
title('Bessel Functions of the Second Kind for v = 0,1,2,3,4')

More About

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The bessely function uses a Fortran MEX-file to call a library developed by D. E Amos [3] [4].






See Also

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