While reading a scientific paper, I have come across a property of modified Bessel function: $$\frac{I_1(az)}{I_0(az)}=\frac{1}{a}\frac{I_1(z)}{I_0(z)}$$ Is this property true? If not, how can the LHS be written in terms of $I_1(z)$ and $I_0(z)$?
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You have significantly changed your question. So that the answer makes sense to future readers I recommend you revert the question and ask your follow up query as a new question. – Ian Miller Oct 01 '16 at 09:41
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My bet is on a continued fraction gone bad & wrong during transcription. – Jack D'Aurizio Oct 01 '16 at 09:42
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Perhaps the OP can provide a link to the scientific paper they were reading to give some more context. – Ian Miller Oct 01 '16 at 09:46
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@IanMiller: Here's the link . But I'm not sure if you'll be able to access. You can get in on sci-hub using the doi (10.1017/S0022112010001540). Warning: the property is not given directly although it can be deduced from eq 4.13 and 4.17 of the paper – Rhinocerotidae Oct 01 '16 at 09:56
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No. Its behind a subscription wall. Maybe you can quote the two equations you have mentioned. – Ian Miller Oct 01 '16 at 10:22
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1@SaravanaKumar: I do not get how your identity follows from 4.13 and 4.17. Probably you exploited some definition and a scale-property of the Fourier (inverse) transform, while the (inverse) Fourier transform used by the authors has a different normalization constant. That is a common issue, see (http://mathworld.wolfram.com/FourierTransform.html): some authors... – Jack D'Aurizio Oct 01 '16 at 14:28
