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I don't really agree with this. I'm not familiar with any functional equations qua equations between linear functionals, for one thing.
Charles Matthews 18:38, 6 Apr 2004 (UTC)
I'm inclined to agree with you. The first item was an example of what I've always thought the term functional equation means, but it's only one example; there are many others. I could list examples, and maybe with effort I could list interesting examples (such as the one that was mentioned before I erased this page), but I'm not sure I know an actual definition of this concept. Michael Hardy 19:00, 6 Apr 2004 (UTC)
There is a little more content here, now. It might be better to merge this all into functional (mathematics), at some point in the future. Maybe just see how it goes. Charles Matthews 08:19, 14 Apr 2004 (UTC)
I know - functional equation used to be a redirect to functional. You say a poor definition. It is certainly quite a challenge to give a complete and formal definition - which would also include all interesting examples, of course. I don't know - there could be functional equations involving convolution? Charles Matthews 16:09, 14 Apr 2004 (UTC)
OK, the gamma function is defined (more-or-less) by some functional equation(s). There is a difficulty, felt at operator for example, that to be a good encyclopedia article you need some abstract talk, as well as examples.
Tell you what, time to look in some rival products. Take the big Soviet encyclopedia of maths. The editorial notes in the English translation actually quarrel with the original article. Says that typical are
also gamma function, Riemann zeta, Yang-Baxter and things like
And more. I'll look in the Japanese encyclopedia, too.
Charles Matthews 15:35, 15 Apr 2004 (UTC)
Thanks for the job! Pfortuny 15:42, 15 Apr 2004 (UTC)
In that (EDM) under Special Functional Equations (no limiting operations), we get
- discontinuous solution of Cauchy equation by Hamel basis for R over Q (Hamel-Lebesgue)
- Jensen equation, when solutions must be continuous
- general addition theorem, result of Picard in the complex plane I - d'Alembert equation, continuous solutions via cosh and cos
- stuff on Schröder, Abel.
So, looks like there really are half-a-dozen basic examples.
Charles Matthews 15:49, 15 Apr 2004 (UTC)
I added some choice words which should help any wayward users exit this page poste haste (do you people ever consider writing something, oh i dunno, useful to people who aren't mathematicians)-- naryathegreat 02:46, Jul 11, 2004 (UTC)
Well, I don't know why you assume this site is for Americans, or by Americans, or to be judged by American standards. As you can see, this article has been discussed by various Wikipedians, with the intention of adding to it. If you looked into it, you'd see that the same people write on other topics. Charles Matthews 18:50, 11 Jul 2004 (UTC)
Well, Americans founded it and the servers are in America, so...but anyway, when i was here last, a subject which i understand well consisted of a cryptic paragraph.:It's better now.-- naryathegreat 01:05, Jul 14, 2004 (UTC)
To the author of ths page: Power function should be: f(x+y) = f(x) * f(y) (rather then f(xy) on the left)
Although this part says nothing but the truth, this solution is not complete. for any positive a is also a solution (as can be quickly checked). The way this result can be achieved is by induction. I'll try to fix that now in one of my own pages. Jotomicron | talk 17:02, 21 February 2006 (UTC)
In Solving functional equations
the real soluction is
f[x] == (Sqrt[x]*C[1])/Sqrt[2]
or
f[x] == -(((-1)^(Log[x]/Log[2])*Sqrt[x]*C[1])/Sqrt[2])
por All x Integer
—Preceding unsigned comment added by 201.58.190.135 ( talk • contribs)
No, x and f(x) are assumed to be real, so sqrt(x) is undefined. googl t 17:02, 31 December 2006 (UTC)
______________________________________________________________________________________________________________________________________________________ just a little thing for f(x+y)^2=f(x)^2+f(y)^2 f does not exist not just for x=-y but for any real x,y f(x+y)^2=f((x+y)+(-y))^2+f(y)^2 f(x+y)^2=f(x+y)^2+f(-y)^2+f(y)^2 0=f(-y)^2+f(y)^2 this isn't much more complicated and it's more accurate. — Preceding unsigned comment added by 94.159.193.2 ( talk) 21:18, 21 May 2015 (UTC)
Hi. If I'm not wrong it is a function not equation. Am I right ?-- Adam majewski ( talk) 09:30, 2 November 2008 (UTC)
Yes. You are right, I was wrong ( probably blind) (:-)) -- Adam majewski ( talk) 16:31, 2 November 2008 (UTC)
Babbage equation $f^n(x)=x, \forall x\in S$ is one classic example. — Preceding unsigned comment added by Scumat ( talk • contribs) 03:24, 31 May 2011 (UTC)
What would be the name of the branch of mathematics ( /info/en/?search=Mathematics_Subject_Classification#First-level_areas) (or say, the typical name of a college class) where functional equations would be studied? Can a little more of that context be added to the intro? DKEdwards ( talk) 19:26, 27 February 2023 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
I don't really agree with this. I'm not familiar with any functional equations qua equations between linear functionals, for one thing.
Charles Matthews 18:38, 6 Apr 2004 (UTC)
I'm inclined to agree with you. The first item was an example of what I've always thought the term functional equation means, but it's only one example; there are many others. I could list examples, and maybe with effort I could list interesting examples (such as the one that was mentioned before I erased this page), but I'm not sure I know an actual definition of this concept. Michael Hardy 19:00, 6 Apr 2004 (UTC)
There is a little more content here, now. It might be better to merge this all into functional (mathematics), at some point in the future. Maybe just see how it goes. Charles Matthews 08:19, 14 Apr 2004 (UTC)
I know - functional equation used to be a redirect to functional. You say a poor definition. It is certainly quite a challenge to give a complete and formal definition - which would also include all interesting examples, of course. I don't know - there could be functional equations involving convolution? Charles Matthews 16:09, 14 Apr 2004 (UTC)
OK, the gamma function is defined (more-or-less) by some functional equation(s). There is a difficulty, felt at operator for example, that to be a good encyclopedia article you need some abstract talk, as well as examples.
Tell you what, time to look in some rival products. Take the big Soviet encyclopedia of maths. The editorial notes in the English translation actually quarrel with the original article. Says that typical are
also gamma function, Riemann zeta, Yang-Baxter and things like
And more. I'll look in the Japanese encyclopedia, too.
Charles Matthews 15:35, 15 Apr 2004 (UTC)
Thanks for the job! Pfortuny 15:42, 15 Apr 2004 (UTC)
In that (EDM) under Special Functional Equations (no limiting operations), we get
- discontinuous solution of Cauchy equation by Hamel basis for R over Q (Hamel-Lebesgue)
- Jensen equation, when solutions must be continuous
- general addition theorem, result of Picard in the complex plane I - d'Alembert equation, continuous solutions via cosh and cos
- stuff on Schröder, Abel.
So, looks like there really are half-a-dozen basic examples.
Charles Matthews 15:49, 15 Apr 2004 (UTC)
I added some choice words which should help any wayward users exit this page poste haste (do you people ever consider writing something, oh i dunno, useful to people who aren't mathematicians)-- naryathegreat 02:46, Jul 11, 2004 (UTC)
Well, I don't know why you assume this site is for Americans, or by Americans, or to be judged by American standards. As you can see, this article has been discussed by various Wikipedians, with the intention of adding to it. If you looked into it, you'd see that the same people write on other topics. Charles Matthews 18:50, 11 Jul 2004 (UTC)
Well, Americans founded it and the servers are in America, so...but anyway, when i was here last, a subject which i understand well consisted of a cryptic paragraph.:It's better now.-- naryathegreat 01:05, Jul 14, 2004 (UTC)
To the author of ths page: Power function should be: f(x+y) = f(x) * f(y) (rather then f(xy) on the left)
Although this part says nothing but the truth, this solution is not complete. for any positive a is also a solution (as can be quickly checked). The way this result can be achieved is by induction. I'll try to fix that now in one of my own pages. Jotomicron | talk 17:02, 21 February 2006 (UTC)
In Solving functional equations
the real soluction is
f[x] == (Sqrt[x]*C[1])/Sqrt[2]
or
f[x] == -(((-1)^(Log[x]/Log[2])*Sqrt[x]*C[1])/Sqrt[2])
por All x Integer
—Preceding unsigned comment added by 201.58.190.135 ( talk • contribs)
No, x and f(x) are assumed to be real, so sqrt(x) is undefined. googl t 17:02, 31 December 2006 (UTC)
______________________________________________________________________________________________________________________________________________________ just a little thing for f(x+y)^2=f(x)^2+f(y)^2 f does not exist not just for x=-y but for any real x,y f(x+y)^2=f((x+y)+(-y))^2+f(y)^2 f(x+y)^2=f(x+y)^2+f(-y)^2+f(y)^2 0=f(-y)^2+f(y)^2 this isn't much more complicated and it's more accurate. — Preceding unsigned comment added by 94.159.193.2 ( talk) 21:18, 21 May 2015 (UTC)
Hi. If I'm not wrong it is a function not equation. Am I right ?-- Adam majewski ( talk) 09:30, 2 November 2008 (UTC)
Yes. You are right, I was wrong ( probably blind) (:-)) -- Adam majewski ( talk) 16:31, 2 November 2008 (UTC)
Babbage equation $f^n(x)=x, \forall x\in S$ is one classic example. — Preceding unsigned comment added by Scumat ( talk • contribs) 03:24, 31 May 2011 (UTC)
What would be the name of the branch of mathematics ( /info/en/?search=Mathematics_Subject_Classification#First-level_areas) (or say, the typical name of a college class) where functional equations would be studied? Can a little more of that context be added to the intro? DKEdwards ( talk) 19:26, 27 February 2023 (UTC)