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I hope this is the right section to post this question.

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 surface given above (for varying n and β), how do I go about ?

Thanks!

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# Line of maximum for a 2D 'surface'

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