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

Started by	"IV" <ivgroups@onlinehome.de>
First post	2018-07-25 13:51 +0200
Last post	2018-07-25 20:12 -0400
Articles	16 — 4 participants

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#695505 — Are there applications with functions of one variable composed of at least two different transcendental functions?

From	"IV" <ivgroups@onlinehome.de>
Date	2018-07-25 13:51 +0200
Subject	Are there applications with functions of one variable composed of at least two different transcendental functions?
Message-ID	<pj9o7m$5kt$1@news.albasani.net>

Hallo,

please forget my former related thread.

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?

Thanks.

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#695511

From	Sergio <invalid@invalid.com>
Date	2018-07-25 09:41 -0500
Message-ID	<pja272$16n3$1@gioia.aioe.org>
In reply to	#695505

On 7/25/2018 6:51 AM, IV wrote:
> Hallo,
> 
> please forget my former related thread.
> 
> 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?
> 
> Thanks.

try   e^(i*x)

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#695517

From	"IV" <ivgroups@onlinehome.de>
Date	2018-07-25 17:19 +0200
Message-ID	<pja4ea$9il$1@news.albasani.net>
In reply to	#695511

"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.

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#695525

From	benj <benj.fake@gmail.com>
Date	2018-07-25 12:24 -0400
Message-ID	<pja87a$1irn$1@gioia.aioe.org>
In reply to	#695517

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?

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#695532

From	"IV" <ivgroups@onlinehome.de>
Date	2018-07-25 19:00 +0200
Message-ID	<pjaab6$8ot$1@news.albasani.net>
In reply to	#695525

"benj"  schrieb im Newsbeitrag news:pja87a$1irn$1@gioia.aioe.org...
> So go with e^sinx.
But which application in physics uses this function?

> What is the real question here anyway?
I'm looking for some examples of applications for using global or local 
inverses and solving equations for composed functions in closed-form 
expressions.

> I seem to recall this same discussion sometime in the past on USENET. Was 
> that you?
No, I wasn't it.

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#695563

From	Sergio <invalid@invalid.com>
Date	2018-07-25 15:30 -0500
Message-ID	<pjamkl$ck8$1@gioia.aioe.org>
In reply to	#695525

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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#695569

From	"IV" <ivgroups@onlinehome.de>
Date	2018-07-25 22:46 +0200
Message-ID	<pjanjm$pns$1@news.albasani.net>
In reply to	#695563

"Sergio"  schrieb im Newsbeitrag news:pjamkl$ck8$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 ... and didn't realize that i is algebraic.
>> So go with e^sinx . Duh.
> 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
Clearly, Sergio, you are right: e^(i*x) = cos(x) + i sin(x). That is a 
function composed of two transcendental functions. I overlooked that in your 
answer, because I'm treating other problems at the moment. I expected  e x p 
l i c i t  expressions with more than one transcendental functions.
I asked for transcendental functions, not for transcendental numbers.

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#695607

From	benj <benj.fake@gmail.com>
Date	2018-07-25 20:05 -0400
Message-ID	<pjb394$urb$1@gioia.aioe.org>
In reply to	#695563

On 7/25/2018 4:30 PM, Sergio wrote:
> 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.
> 
Um, yes. A curve because at first glance xi is not complex and appears 
to only be imaginary. The catch of course is that yes indeed x could be 
complex.

However if xi is simply imaginary. then we find online:
-=-=-=-=
"Well, we know that i^2 = −1, so i is the solution to:

x^2 + 1 = 0

When x = i we get −1 + 1 = 0

So the imaginary number i is an Algebraic Number"
-=-=-=-=-=
However if x is a complex number it changes things.

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#695536

From	Libor Striz <poutnik4REMOVEnntp@CAPITALSgmail.com>
Date	2018-07-25 19:35 +0200
Message-ID	<pjaccm$937$1@dont-email.me>
In reply to	#695517

"IV" <ivgroups@onlinehome.de> Wrote in message:

>> 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.
> 
As e^(i*x)= cos(x) + i*sin(x),
It implicitly  contains 2 transcendental functions.

Another example is an attenuating oscillation.

y(t)=A*exp(-B*t)*sin(omega*t+file)


But I like to know, what is the background  of your question ?
It looks quite abstract, like solving a homework or an exam question.

-- 
Libor Striz aka Poutnik ( a pilgrim/wanderer/wayfarer)

"Humour is the only effective weapon against stupidity."
Miloš Forman


----Android NewsGroup Reader----
http://usenet.sinaapp.com/

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#695553

From	"IV" <ivgroups@onlinehome.de>
Date	2018-07-25 21:32 +0200
Message-ID	<pjaj80$3qt$1@news.albasani.net>
In reply to	#695536

"Libor Striz"  schrieb im Newsbeitrag news:pjaccm$937$1@dont-email.me...
>>> 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.
> As e^(i*x)= cos(x) + i*sin(x), It implicitly  contains 2 transcendental 
> functions.
Yes, you are right. But each function can be decomposed into more than one 
transcendental functions together with or without algebraic functions.

> Another example is an attenuating oscillation.
> y(t)=A*exp(-B*t)*sin(omega*t+file)
Oh yes, that's fine. Thanks.

> But I like to know, what is the background  of your question ?
I already wrote here:
I'm looking for some examples of applications for using global or local 
inverses and solving equations for composed functions in closed-form 
expressions.
For functions of only one variable.

> It looks quite abstract, like solving a homework or an exam question.
It looks so abstract like mathematics is.
I want to create a method/theory for calculating the inverse or to solve 
equations of transcendental functions of one variable symbolically, means in 
closed-form.
I already have some theorem.
Now I want to see if such a method/theory could be useful also in 
applications. I found: it is.

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#695522

From	benj <benj.fake@gmail.com>
Date	2018-07-25 11:53 -0400
Message-ID	<pja6em$1fbl$1@gioia.aioe.org>
In reply to	#695511

On 7/25/2018 10:41 AM, Sergio wrote:
> On 7/25/2018 6:51 AM, IV wrote:
>> Hallo,
>>
>> please forget my former related thread.
>>
>> 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?
>>
>> Thanks.
> 
> try   e^(i*x)
> 
Wassmatta "Kensi". Didn't your imaginary Ph.D let you find this answer 
on CNN or in The Guardian? You really are nothing but an ignorant 
journalists, right?

Sergio = 1
Lying "Kensi" = 0

(as usual)

*Snicker*

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#695531

From	"IV" <ivgroups@onlinehome.de>
Date	2018-07-25 18:54 +0200
Message-ID	<pjaa05$qae$1@news.albasani.net>
In reply to	#695522

"benj"  schrieb im Newsbeitrag news:pja6em$1fbl$1@gioia.aioe.org... 
> Sergio ...
This is off topic.

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#695558

From	Sergio <invalid@invalid.com>
Date	2018-07-25 14:41 -0500
Message-ID	<pjajor$751$1@gioia.aioe.org>
In reply to	#695531

On 7/25/2018 11:54 AM, IV wrote:
> "benj"  schrieb im Newsbeitrag news:pja6em$1fbl$1@gioia.aioe.org...
>> Sergio ...
> This is off topic.

OT is math, not physics

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#695561

From	"IV" <ivgroups@onlinehome.de>
Date	2018-07-25 22:12 +0200
Message-ID	<pjalk4$tnd$1@news.albasani.net>
In reply to	#695558

"Sergio"  schrieb im Newsbeitrag news:pjajor$751$1@gioia.aioe.org... 
>>> "benj"  schrieb im Newsbeitrag news:pja6em$1fbl$1@gioia.aioe.org...
>>> Sergio ...
>> This is off topic.
> OT is math, not physics
You misunderstood. benj's attacks are OT.
Physical applications of mathematics aren't OT here.
No further comment necessary.

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#695588

From	Sergio <invalid@invalid.com>
Date	2018-07-25 16:46 -0500
Message-ID	<pjar3d$jgg$1@gioia.aioe.org>
In reply to	#695561

On 7/25/2018 3:12 PM, IV wrote:
> "Sergio"  schrieb im Newsbeitrag news:pjajor$751$1@gioia.aioe.org...
>>>> "benj"  schrieb im Newsbeitrag news:pja6em$1fbl$1@gioia.aioe.org...
>>>> Sergio ...
>>> This is off topic.
>> OT is math, not physics
> You misunderstood. benj's attacks are OT.
> Physical applications of mathematics aren't OT here.
> No further comment necessary.

not sure how I put OT in there-- should have been "this" and not "OT"
anyhow it is interesting area(s)

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#695608

From	benj <benj.fake@gmail.com>
Date	2018-07-25 20:12 -0400
Message-ID	<pjb3kd$v9b$1@gioia.aioe.org>
In reply to	#695588

On 7/25/2018 5:46 PM, Sergio wrote:
> On 7/25/2018 3:12 PM, IV wrote:
>> "Sergio"  schrieb im Newsbeitrag news:pjajor$751$1@gioia.aioe.org...
>>>>> "benj"  schrieb im Newsbeitrag news:pja6em$1fbl$1@gioia.aioe.org...
>>>>> Sergio ...
>>>> This is off topic.
>>> OT is math, not physics
>> You misunderstood. benj's attacks are OT.
>> Physical applications of mathematics aren't OT here.
>> No further comment necessary.
> 
> not sure how I put OT in there-- should have been "this" and not "OT"
> anyhow it is interesting area(s)
> 
Benj's "attacks"? Did you see any "attack" here?
I'm just trying to get our resident PhD "kensi" to put down the
Guardian and help us all out with this minor discussion of number 
theory. I thought she was interested in physics applications of 
mathematics?

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csiph-web

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

Contents

#695505 — Are there applications with functions of one variable composed of at least two different transcendental functions?

#695511

#695517

#695525

#695532

#695563

#695569

#695607

#695536

#695553

#695522

#695531

#695558

#695561

#695588

#695608