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X tan(x) and it's inverse

  1. Nov 10, 2006 #1
    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. jcsd
  3. Nov 10, 2006 #2

    arildno

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    Galumba-floop numbers, perhaps?
    In other words, you are free to invent your own names.
     
  4. Nov 10, 2006 #3

    Office_Shredder

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    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?
     
  5. Nov 11, 2006 #4
    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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