I would like to find derivations of exp(-ik(adsbygoogle = window.adsbygoogle || []).push({}); _{0}r) respect to k in order to calculate exp(-ik_{1}r) by using Taylor expansion:

exp(-ik_{1}r) = (exp(-ik_{0}r))^{(0)}+(k_{1}-k_{0})(exp(-ik_{0}r))^{(1)}/1! + (k_{1}-k_{0})^{2}(exp(-ik_{0}r))^{(2)}/2! + ...

This expansion converges when the value of r is relative low (0.3 - 1.2). However, when r grows with larger value (100-1000), the expansion does not converge any more.

k_{0}= 21

k_{1}= 27

Is there any solution to find exp(ik_{1}r) by using Taylor expansion for larger r?

Thank you very much

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# Derivation of imaginary exponential function

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