[seqfan] Re: Integer ratios between asinh at integer arguments

[israel at math.ubc.ca]

What's going on here is that T_n(i sinh(x)) = i^n sinh(n x) for odd 
integers n and i^n cosh(n x) for even integers n, where T_n is the n'th 
Chebyshev polynomial of the first kind.

Robert Israel
University of British Columbia

On Mar 15 2013, Gottfried Helms wrote:

>Dear seqfans -
>
>just by incident I cam across a set of integer relations between
>sinh(n) and cosh(n) at integer arguments n.
>
>A quick look at OEIS for some of the occuring sequences
>gave nice results and cross-relations to many different
>areas. It would surely be useful, if the occuring sequences
>could be related by their common focus. Unfortunately
>I am and shall be busy with other things, so I can't
>go for enriching/updating all the comments.
>
>I've put my findings together in a small compilation in
>
>http://go.helms-net.de/math/divers/asinh_integer_ratios.pdf
>
>Perhaps someone else is able to inject that information.
>
>Sorry again, but I'm also of very weak health this monthes...
>
>Gottfried Helms
>
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