INTRODUCING THE MRB CONSTANT: CONVERGENCE, GEOMETRY, AND OPEN PROBLEMS

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Norozpour Sıgaroodı S., Ray Burn M.

INTERNATIONAL 10th USBILIM APPLIED SCIENCES CONGRESS , Dubai, United Arab Emirates, 8 - 12 November 2025, pp.384, (Summary Text)

  • Publication Type: Conference Paper / Summary Text
  • City: Dubai
  • Country: United Arab Emirates
  • Page Numbers: pp.384
  • Open Archive Collection: AVESIS Open Access Collection
  • Istanbul Gelisim University Affiliated: Yes

Abstract

The MRB constant, recently introduced by Marvin Ray Burns, emerges from the alternating series of n^ (1/n) and exhibits deep connections with both analytic number theory and high-dimensional geometry. This talk introduces the constant’s definition, its convergence properties, and its geometric interpretation in terms of n-dimensional hypercubes. We also discuss numerical methods for computing the constant, including splitting of series, asymptotic analysis, and integral representations. Emphasis will be placed on the constant’s potential role as a bridge between series analysis, geometry, and special functions. The presentation will outline key starting points for further exploration and highlight ongoing collaborative work aimed at formalizing these results within the framework of modern mathematical research.