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Implementation of the Combined--Nonlinear Condensation Transformation

S. V. Aksenov, M. A. Savageau, U. D. Jentschura, J. Becher, G. Soff, P. J. Mohr

Abstract

We discuss several applications of the recently proposed combined nonlinear-condensation transformation (CNCT) for the evaluation of slowly convergent, nonalternating series. These include certain statistical distributions which are of importance in linguistics, statistical-mechanics theory, and biophysics (statistical analysis of DNA sequences). We also discuss applications of the transformation in experimental mathematics, and we briefly expand on further applications in theoretical physics. Finally, we discuss a related Mathematica program for the computation of Lerch's transcendent.

Implementation of the Combined--Nonlinear Condensation Transformation

Abstract

We discuss several applications of the recently proposed combined nonlinear-condensation transformation (CNCT) for the evaluation of slowly convergent, nonalternating series. These include certain statistical distributions which are of importance in linguistics, statistical-mechanics theory, and biophysics (statistical analysis of DNA sequences). We also discuss applications of the transformation in experimental mathematics, and we briefly expand on further applications in theoretical physics. Finally, we discuss a related Mathematica program for the computation of Lerch's transcendent.

Paper Structure

This paper contains 9 sections, 69 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. The Combined Nonlinear--Condensation Transformation
  3. CNCT: Motivation
  4. CNCT: Formulas
  5. Applications to Special Functions used in Statistics
  6. An Application in Experimental Mathematics
  7. Other Applications of the CNCT
  8. Conclusions
  9. Mathematica Program for Lerch's Transcendent

Figures (1)

  • Figure 1: A Mathematica program for the calculation of Lerch's transcendent using the CNC transformation. A line-by-line explanation is in the text.