Mathematical formulations of Bradford's law derived from relationships among bibliometric laws

This paper describes the result of following two kinds of studies. 1) to derive a similarity among some bibliometric laws 2) to mathematically represent Bradford's law based on the similarity and to show the adequacy of the representation. In terms of the first study, it was shown that a similarity which unified these laws was identified, and that Mandelbrot's law was a general form of Zipf's law. On the other hand, the mathematical representation of Bradford's law traditionally used was not strictly coincided with an integral approximation to the summation of Zipf's or Mandelbrot's laws. Therefore, the author derived a new mathematical representation of Bradford's law and examined successfully its validity by the data used for having shown traditional representions.