       Re: Sinh[y]/y as y->0?

• To: mathgroup at smc.vnet.net
• Subject: [mg33458] Re: Sinh[y]/y as y->0?
• From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
• Date: Fri, 22 Mar 2002 04:06:33 -0500 (EST)
• References: <a7csli\$i0t\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```aes <siegman at stanford.edu> wrote:
> A particular calculation produces at an early stage the intermediate
> result
>
>    p1 = (Sin[x]/x) + (Sinh[y]/y) ,        (x and y both real)
>
> and this result then feeds into further expressions in a lengthy symbolic
> calculation.
>
> When I try to do any numerical evaluations of the final expressions with
> either x or y = 0, I get "Indeterminate expression" or "infinity 1/0"
> error messages, even though the expressions themselves, like the
> expression above, are perfectly determinate and finite for those limits.

The "expressions themselves" are normally considered to be undefined at 0.
OTOH, as their arguments approach 0, their _limits_ are indeed "perfectly
determinate and finite". You should not expect a function's value (or
lack thereof) _at_ x = c to be related to the limit of that function as
x _approaches_ c.

> Any simple way to make this expression behave as it should under
> numerical evaluation?

AFAIK, there is no way to do what you want. And, in my opinion, what you
want to be done under numerical evaluation is not what should be done.

Can you reasonably well work with the limits of the expressions, rather
than their simple numerical evaluations?

David Cantrell

--

```

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