Dear forum members,
I am encountering the problem related to finding derivations of Hankel functions presented below and would you please suggest me any idea for the problem if possible?
I would like to find derivations of H0(2)(k0.r) respect to k0 and I found a recursive relation to find its derivatives can be found in the attachment.
And then I will calculate H0(2)(k1.r) by using Taylor expansion:
H0(2)(k1.r) = ( H0(2)(k0.r))[0] + (k1-k0). ( H0(2)(k0.r))[1]/1! + (k1-k0)2. ( H0(2)(k0.r))[2]/2!+ ....
However, the result only converge with small value of r (0.3 - 1.2) and it will diverge if r is large (100-1000)
k0=21
k1=27
Could you please propose me any idea for finding derivatives of Hankel function for large r in order to make the result converge?
Thank you very much
derivatives.doc
