Some Further Developments in the Infinite Product Representation of Elementary Functions

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Viktor Reshniak
Viktor Reshniak
Ξ± Middle Tennessee State University Middle Tennessee State University

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Some Further Developments in the Infinite Product Representation of Elementary Functions

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Abstract

An innovatory approach has been recently proposed for the derivation of infinite product representation of elementary functions. The approach is based on the comparison of different alternative forms of Green’s functions for boundary-value problems stated for the twodimensional Laplace equation. A number of new infinite product representations of elementary functions was actually derived within the scope of that approach. The present study continues the trend: it aims at an analysis of the approach and exploring ways for its extending to some other problem statements that might also be efficiently treated.

References

8 Cites in Article
  1. C Caratheodory (1969). Conformal representation.
  2. Z Nehari (1952). Conformal mapping.
  3. I Gradshteyn,I Ryzhik (1980). DETERMINANTS.
  4. Dean Duffy (2001). Green's Functions with Applications.
  5. R Haberman (2012). Applied Partial Differential Equations with Fourier Series and Boundary Value Problems.
  6. A Yu,Melnikov (2008). A new approach to the representation of some trigonometric and hyperbolic functions by infinite products.
  7. Yuri Melnikov (2011). Infinite Products and Elementary Functions.
  8. P Morse,H Feshbach (1953). Methods of Theoretical Physics.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Viktor Reshniak. 2013. \u201cSome Further Developments in the Infinite Product Representation of Elementary Functions\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 13 (GJSFR Volume 13 Issue F4): .

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Version of record

v1.2

Issue date

May 25, 2013

Language
en
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An innovatory approach has been recently proposed for the derivation of infinite product representation of elementary functions. The approach is based on the comparison of different alternative forms of Green’s functions for boundary-value problems stated for the twodimensional Laplace equation. A number of new infinite product representations of elementary functions was actually derived within the scope of that approach. The present study continues the trend: it aims at an analysis of the approach and exploring ways for its extending to some other problem statements that might also be efficiently treated.

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Some Further Developments in the Infinite Product Representation of Elementary Functions

Viktor Reshniak
Viktor Reshniak Middle Tennessee State University

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