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

[ianbell]

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.

 

[arildno]

Galumba-floop numbers, perhaps?
In other words, you are free to invent your own names.

 

[Office_Shredder]

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?

 

[ianbell]

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.