Re: Are there applications with functions of one variable composed of at least two different transcendental functions?

From	Sergio <invalid@invalid.com>
Newsgroups	sci.physics
Subject	Re: Are there applications with functions of one variable composed of at least two different transcendental functions?
Date	2018-07-25 15:30 -0500
Organization	Aioe.org NNTP Server
Message-ID	<pjamkl$ck8$1@gioia.aioe.org> (permalink)
References	<pj9o7m$5kt$1@news.albasani.net> <pja272$16n3$1@gioia.aioe.org> <pja4ea$9il$1@news.albasani.net> <pja87a$1irn$1@gioia.aioe.org>

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On 7/25/2018 11:24 AM, benj wrote:
> On 7/25/2018 11:19 AM, IV wrote:
>> "Sergio"  schrieb im Newsbeitrag news:pja272$16n3$1@gioia.aioe.org...
>>>> Are there applications in physics in which a closed-form expression
>>>> exists for a function of one variable, where the function is a
>>>> function composed of at least two different transcendental functions?
>>>> Could you please name here some examples of such applications?
>>> try   e^(i*x)
>> Clearly, but this function term contains only one transcendental
>> function: x \mapsto e^x. x \mapsto i*x is algebraic, not transcendental.
>>
> 
> 
> Unfortunately Sergio did the "kensi" stumble and didn't realize that i
> is algebraic.
> 
> So go with e^sinx . Duh.
> 
> What is the real question here anyway? I seem to recall this same
> discussion sometime in the past on USENET. Was that you?
> 
> 

I threw a curve ball to see what he would do, open the door for ideas,
etc, x could be complex, or Pi, or Pi^(x*i)

  anyhow I dug this up from wiki -

Transcendental number
From Wikipedia, the free encyclopedia

In mathematics, a transcendental number is a real or complex number that
is not algebraic—that is, it is not a root of a nonzero polynomial
equation with integer (or, equivalently, rational) coefficients. The
best-known transcendental numbers are π and e. Though only a few classes
of transcendental numbers are known (in part because it can be extremely
difficult to show that a given number is transcendental), transcendental
numbers are not rare. Indeed, almost all real and complex numbers are
transcendental, since the algebraic numbers are countable while the sets
of real and complex numbers are both uncountable. All real
transcendental numbers are irrational, since all rational numbers are
algebraic. The converse is not true: not all irrational numbers are
transcendental; e.g., the square root of 2 is irrational but not a
transcendental number, since it is a solution of the polynomial equation
x2 − 2 = 0. Another irrational number that is not transcendental is the
golden ratio, φ {\displaystyle \varphi } \varphi or ϕ {\displaystyle
\phi } \phi , since it is a solution of the polynomial equation x2 − x −
1 = 0.

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