How to implement following bessel function in MATLAB

help besselk
 BESSELK Modified Bessel function of the second kind.
    K = BESSELK(NU,Z) is the modified Bessel function of the second kind,
    K_nu(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.
 
    K = BESSELK(NU,Z,SCALE) returns a scaled K_nu(Z) specified by SCALE:
        0 - (default) is the same as BESSELK(NU,Z)
        1 -  scales K_nu(Z) by exp(Z)
 
    Class support for inputs NU and Z:
       float: double, single
 
    See also AIRY, BESSELH, BESSELI, BESSELJ, BESSELY.

    Documentation for besselk
       doc besselk

    Other uses of besselk

       codistributed/besselk    sym/besselk    symbolic/besselk
       gpuArray/besselk

What does the very first line say? Modified Bessel function of the second kind. So, yes.

The order nu, is M_0-i-j. You did that.

The argument, z, you gave as:

(2*(sqrt(((m_1)+(m_2))*(m_0))))

The only thing I would do is CUT THE PARENS! Having too many parens can make your code impossible to read. This next does as well:

2*sqrt((m_1 + m_2)*m_0)

Really, did you really need parens around each variable name?

A = besselk(m_0 - i - j, 2*sqrt((m_1 + m_2)*m_0));

Even the artful use of whitespace can make your code more easily read. And since you will need to read your own code to be able to debug that code, that is important.

If you cannot even read your own code, that should tell you something.