X tan(x) and it's inverse

1. Nov 10, 2006

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.

2. Nov 10, 2006

arildno

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

3. Nov 10, 2006

Office_Shredder

Staff Emeritus
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?

4. Nov 11, 2006

ianbell

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.