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garserdt216
garserdt216
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Often times, we consult resources, like Abramowitz and Stegun's Handbook of Mathematical Functions https://www.math.ubc.ca/~cbm/aands/, NIST's database on special functions https://www.nist.gov/programs-projects/special-functions, or Mathematica to find identities which aid us with some kind of computation.

However, what if we want to know if we have found a new identity, want to systematically check against the above resources, and want to add to the library? As a simple example, I found

$\lim_{N\to\infty}\sum_{j=0}^N {2j \choose j} \left(\frac{\cos(x)}{2}\right)^{2j}$

converges pointwise to $|\mathrm{csc}(x)|.$ I don't see a representation of this type in the resources provided above.

My questioncase the identity is: How do we add to libraries of special function identities new? Also, and are there journals which, even today, still consider mathematical effort toward discovering identities of classical functions?

Often times, we consult resources, like Abramowitz and Stegun's Handbook of Mathematical Functions https://www.math.ubc.ca/~cbm/aands/, NIST's database on special functions https://www.nist.gov/programs-projects/special-functions, or Mathematica to find identities which aid us with some kind of computation.

However, what if we want to know if we have found a new identity and want to add to the library? As a simple example, I found

$\lim_{N\to\infty}\sum_{j=0}^N {2j \choose j} \left(\frac{\cos(x)}{2}\right)^{2j}$

converges pointwise to $|\mathrm{csc}(x)|.$ I don't see a representation of this type in the resources provided above.

My question is: How do we add to libraries of special function identities, and are there journals which, even today, still consider mathematical effort toward discovering identities of classical functions?

Often times, we consult resources, like Abramowitz and Stegun's Handbook of Mathematical Functions https://www.math.ubc.ca/~cbm/aands/, NIST's database on special functions https://www.nist.gov/programs-projects/special-functions, or Mathematica to find identities which aid us with some kind of computation.

However, what if we want to know if we have found a new identity, want to systematically check against the above resources, and want to add to the library in the case the identity is new? Also, are there journals which, even today, still consider mathematical effort toward discovering identities of classical functions?

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garserdt216
garserdt216
  • 243
  • 1
  • 7

How to determine if you've discovered a new identity for a special function

Often times, we consult resources, like Abramowitz and Stegun's Handbook of Mathematical Functions https://www.math.ubc.ca/~cbm/aands/, NIST's database on special functions https://www.nist.gov/programs-projects/special-functions, or Mathematica to find identities which aid us with some kind of computation.

However, what if we want to know if we have found a new identity and want to add to the library? As a simple example, I found

$\lim_{N\to\infty}\sum_{j=0}^N {2j \choose j} \left(\frac{\cos(x)}{2}\right)^{2j}$

converges pointwise to $|\mathrm{csc}(x)|.$ I don't see a representation of this type in the resources provided above.

My question is: How do we add to libraries of special function identities, and are there journals which, even today, still consider mathematical effort toward discovering identities of classical functions?