The Geometric Interpretation of Some Mathematical Expressions Containing the Riemann ζ-Function
Issue:
Volume 2, Issue 6, December 2016
Pages:
42-46
Received:
6 October 2016
Accepted:
10 November 2016
Published:
17 December 2016
DOI:
10.11648/j.ml.20160206.11
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Abstract: The article discusses some of the mathematical results widely used in practice which contain the Riemann ζ-function, and, at first glance, are in contradiction with common sense. A geometric approach is suggested, based on the concept of the curvature of space, in which is calculated an algorithm that specifies the representation of ζ-function as an infinite diverging series. The analysis is based on the use of Einstein equations to calculate the metric of curved space-time. The solution of the Einstein equations is a metric that has a singularity, like the metric in the vicinity of the black hole. The result can be interpreted in the spirit of a Turing machine that performs the proposed algorithm for calculating the sum of a divergent series.
Abstract: The article discusses some of the mathematical results widely used in practice which contain the Riemann ζ-function, and, at first glance, are in contradiction with common sense. A geometric approach is suggested, based on the concept of the curvature of space, in which is calculated an algorithm that specifies the representation of ζ-function as a...
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Relations Among Certain Generalized Hyper-Geometric Functions Suggested by N-fractional Calculus
Issue:
Volume 2, Issue 6, December 2016
Pages:
47-57
Received:
27 August 2016
Accepted:
19 November 2016
Published:
20 December 2016
DOI:
10.11648/j.ml.20160206.12
Downloads:
Views:
Abstract: The subject of fractional calculus has gained importance and popularity during the past three decades. Based upon the N-fractional calculus we introduce a new N-fractional operators involving hyper-geometric function. By means of these N-fractional operators a number of operational relations among the hyper-geometric functions of two, three, four and several variables are then found. Other closely-related results are also considered.
Abstract: The subject of fractional calculus has gained importance and popularity during the past three decades. Based upon the N-fractional calculus we introduce a new N-fractional operators involving hyper-geometric function. By means of these N-fractional operators a number of operational relations among the hyper-geometric functions of two, three, four a...
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