It is common knowledge that 1st order Macdonald function [tex]K_{1} (z)[/tex] has following asymptotic behavior if [tex]Re (z) > 0[/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]z K_{1} (z) \rightarrow 1 \ \mathrm{if} \ z \rightarrow 0[/tex],

[tex]\sqrt{z} e^{z} K_{1} (z) \rightarrow \sqrt{\frac{\pi}{2}} \ \mathrm{if} \ z \rightarrow \infty[/tex]

I am interesting in a question, how to find following constraint from only asymptotic relations which are indicated above

[tex]|K_{1} (z)| \leq \mathrm{const} \cdot (|z|^{ -1/2 } + |z|^{ -1 }) e^{ - Re (z) }[/tex]

( I cannot find an explanation in the 'H.Bateman, Higher Transcendental Functions'. Thanks)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Macdonald function evaluation

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**