hankel negative order
 

HI all, I am using hankel functions, and come across a probelm in Matlab while applying for negative order. eg: besselh(-7,0.05)

ans =

-2.2976e-003 +3.7553e+013i

But i found some error when checked using the formula given in Abramowitz & Stegun (class 9.16) which is the source for this H(-n,z) = exp(n*pi*i)*H(n,z) where n is order and z is argument

>> exp(7*pi*i)*besselh(7,0.05)

ans =

2.9895e-002 +3.7553e+013i

even though the imaginary part is same..there is some error in real part.For certain orders this is working good in matlab. can any one comment on this which one to use.. Is there any fortran code to handle negative order

sankar.

Re: hankel negative order
 

A play with a calculator should make you suspicious since

H_n(x) = J_n(x) + iY_n(x)

Now for n=7 and x=0.05 we expect J_n(x)~1.21e-15 and Y_n(x)~-3.755e+13 (lead order term in asympotic series as x->0 - which is a good approximation because of the relative largeness of n).

Now exp(i.n.pi) = -1 so H_n(x)~-1.21e-15 + i.3.755e+13.

Tom.