Naming the Solutions for x tan(x) = k: Inventing Our Own Notations?

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SUMMARY

The function f(x) = x tan(x) does not have a widely recognized name, but participants in the discussion propose creative alternatives for the solutions to the equation x tan(x) = k, particularly for integer k. One suggestion is the "Office_Shredder numbers," named after a mathematician who approximated their solutions in 1972. Another proposed name is the "k-th Bellian function of y," denoted as Beta_k(y), which distinguishes it from other functions like Bessel and Beta functions. The discussion emphasizes the freedom to invent notations for mathematical concepts.

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ianbell
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Does the function f(x) = x tan(x) have a name? I am particularly interested in the solutions to x tan(x) = k for integer k. Do these numbers have an accepted name or notation?

TIA.
 
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Galumba-floop numbers, perhaps?
In other words, you are free to invent your own names.
 
They're actually called the Office_Shredder numbers, in honor of the great mathematician Office_Shredder, who discovered a numerical approximation for their solution in 1972.

That's my story, and I'm sticking to it. Why do you need to know?
 
arildno said:
In other words, you are free to invent your own names.

Oh well in that case, in the absence of provenance for the Office-Shredder claim, I dub the unique solution to x tan(x)=y in
[(k-half)pi,(k+half)pi] for nonzero integer k to be the k-th Bellian function of y.
Written capital Beta sub k (y) to distinguish from the Bessel and Bell and , er, Beta functions.

For k=0 we have two equal and opposite solutions for y>0 and none for y<0.
 

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