How would someone verify if a function is 'new' to maths?

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In summary: I completed it two days ago and only verified it was correct yesterday. I know a Professor in the math department and will go to chew on his ear Monday.
  • #1
mesa
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If someone believed they created a new general solution for infinite series summations how should they go about verifying if it is indeed unique?
 
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  • #2
If you are working in an area where you do not have expertise, you should ask one or two mathematicians with expertise in that area. If your result is well-known, they will probably recognize it. If they aren't sure, they will at least know what terms to use to search to see if someone else has found it.

[Note: I assume you aren't an expert, because if you had expertise in the area, then you would already know how to effectively search the literature yourself, and if that were the case, you wouldn't be asking the question.]
 
  • #3
eigenperson said:
If you are working in an area where you do not have expertise, you should ask one or two mathematicians with expertise in that area. If your result is well-known, they will probably recognize it. If they aren't sure, they will at least know what terms to use to search to see if someone else has found it.

[Note: I assume you aren't an expert, because if you had expertise in the area, then you would already know how to effectively search the literature yourself, and if that were the case, you wouldn't be asking the question.]

Your assumptions are correct, I am just a simple Engineering student. I am having a difficult time locating experts in classical analysis in regards to infinite series summations. Do you know of any? Or perhaps have some suggestions on where I should look?

It seems much of modern mathematics deals with subjects that are more 'specialized' and/or abstract. I've looked through the classical analysis section on arXiv but didn't find much.

As far as I can tell 'general solutions' are comparatively rare compared to single valued infinite series so I imagine it would be obvious to anyone in the field if it is currently known.
 
  • #4
Have you asked your engineering professors who could be a good person to contact?
 
  • #5
If the series are generalized hypergeometric series, talk to someone who studies hypergeometric functions.

If the series are combinatorial in origin, talk to a combinatorialist.

If the series are zeta function-like, consider talking to a number theorist.

Otherwise, talk to someone with the goal of figuring out exactly who you should talk to next.
 
  • #6
lisab said:
Have you asked your engineering professors who could be a good person to contact?

I asked an old Professor and he believed it is unique however he also said it would be good to investigate further since this is not his area of expertise. I have another Professor I will be showing it to come Monday, hopefully he will have more insight.

eigenperson said:
If the series are generalized hypergeometric series, talk to someone who studies hypergeometric functions.

If the series are combinatorial in origin, talk to a combinatorialist.

If the series are zeta function-like, consider talking to a number theorist.

I used it to re-write the Basel functions to try to derive 'exact value functions' for their summations. So far there are 3 of them but the best of them will only calculate for exponents s = 4, 6, 8, 10, 12 and the other two for 2,4,6, and 8 for 'exact values' of the summations. It is a bizarre phenomena.

eigenperson said:
Otherwise, talk to someone with the goal of figuring out exactly who you should talk to next.

I agree, thank goodness for PF :)
 
Last edited:
  • #7
Isn't there a Math Department at your school? Go find a math prof.
 
  • #8
Integral said:
Isn't there a Math Department at your school? Go find a math prof.

I completed it two days ago and only verified it was correct yesterday. I know a Professor in the math department and will go to chew on his ear Monday.
 
  • #9
mesa said:
I used it to re-write the Basel functions to try to derive 'exact value functions' for their summations. So far there are 3 of them but the best of them will only calculate for exponents s = 4, 6, 8, 10, 12 and the other two for 2,4,6, and 8 for 'exact values' of the summations. It is a bizarre phenomena.

To be clear, is this what you are talking about:

http://en.wikipedia.org/wiki/Basel_problem

and how it applies to the Riemann zeta function?
 
  • #10
SteamKing said:
To be clear, is this what you are talking about:

http://en.wikipedia.org/wiki/Basel_problem

and how it applies to the Riemann zeta function?

That's correct. I started a couple threads on it not too long ago.

I mentioned it here because the tool I used was an earlier version of the now finished summation function, and that in turn came from another thread where I was playing with infinite series summations for 'e' and someone jokingly said I should find a series equal to '1' and multiply it by 'e'.

After figuring out a series summation for '1' and multiplying by 'e' (thought it would be fun to respond) I saw something and started down the path that eventually led me here.
 

Related to How would someone verify if a function is 'new' to maths?

1. How do you define a "new" function in mathematics?

A "new" function in mathematics refers to a function that has not been previously discovered or defined. It is unique and has not been studied or used before in mathematical equations or theories.

2. How can someone verify if a function is truly "new" to mathematics?

One way to verify if a function is "new" to mathematics is to research existing literature and publications to see if it has been mentioned or used before. If there is no record of the function being studied or used, it can be considered "new" to mathematics.

3. Is there a specific process or criteria for determining if a function is "new" in mathematics?

While there is no specific process or criteria, a function can be considered "new" in mathematics if it is not a variation or combination of existing functions, and if it provides new insights or solutions to mathematical problems.

4. Can a function be considered "new" if it has been used in other fields or industries?

Yes, a function can still be considered "new" in mathematics even if it has been used in other fields or industries. As long as it has not been previously studied or applied in mathematical theories or equations, it can be considered "new" to the field of mathematics.

5. Are there any notable examples of "new" functions in mathematics?

Yes, there are many notable examples of "new" functions in mathematics, such as the Ackermann function, the Busy Beaver function, and the Skewes' number function. These functions have provided new insights and solutions to mathematical problems and have not been previously discovered or defined.

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