- #1
mesa
Gold Member
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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?
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.]
lisab said:Have you asked your engineering professors who could be a good person to contact?
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.
eigenperson said:Otherwise, talk to someone with the goal of figuring out exactly who you should talk to next.
Integral said:Isn't there a Math Department at your school? Go find a math prof.
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.
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?
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.
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.
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.
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.
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.