# Disk Harmonic Functions (Scripts) 1.0

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• Last update: 6 years ago
• Price: Free |
• Operating system: Linux, Mac OS X, Win All, BSD, Solaris
• Publisher: Carey Smith (6 other programs)
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## Disk Harmonic Functions (Scripts) Publisher's description

### Computes Disk Harmonic Functions; uses Bessel functions and derivatives Requires BessDerivZerosBisect2.m

Computes Disk Harmonic Functions; uses Bessel functions and derivatives
Requires BessDerivZerosBisect2.m
function dnm = DiskHarmonic(m,n,r,theta)
if(m == 0)
dnm = 1*Rnm
elseif(m < 0)
dnm = sqrt(2)*Rnm.*sin(mu*theta)
elseif(m > 0)
dnm = sqrt(2)*Rnm.*cos(mu*theta)
end
m<0: dnm(r,theta) = sqrt(2)*Rnm(r)*sin(m*theta) (mu = |m|)
m=0: dnm(r,theta) = 1*R_n0(r) (mu = |m|)
m>0: dnm(r,theta) = sqrt(2)*Rnm(r)*cos(m*theta) (m = |mu|)

n = 0,1,2,...
m = ...-2,-1,0,1,2... (Does not appear to be a requirement the m<=n
r & theta are vectors of polar coordinates of individual points (not a grid)
Rnm(r) = anm*J_m(knm*r)
where
J_m(r) is a Bessel function of the first kind
knm = a spatial freq. = the nth positive root of d/dr(J_m(r)) = 0
anm = 1/sqrt((1-(m/knm)^2)*(J_m(knm))) for n>0 or m>0 (a_00=1)
For n=0, m=0: d_00=1 (a00=1, J0(0)=1, R00=1) (piston term)

#### System Requirements:

MATLAB 7.10 (2010a)
Program Release Status: New Release
Program Install Support: Install and Uninstall

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