Hello,(adsbygoogle = window.adsbygoogle || []).push({});

While analysing the asymptotic value of a ratio of a bessel and a hankel function, I reduced it to something of the form

[(1 + β/n)^ n * (1 + n/β)^ β] / 2^(n+β) ; n and β are integers and greater than 1

how do I show that the above expression is always less than 1, for n≠β. When n=β, the above expression becomes equal to 1.

Or relatedly, if I have to find the line of maximum for a 2D expression given above (for varying n and β), how do I go about ?

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!

# Functional analysis (?)

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