Some Further Developments in the Infinite Product Representation of Elementary Functions

Viktor Reshniak

Some Further Developments in the Infinite Product Representation of Elementary Functions

Viktor Reshniak * §

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§ Middle Tennessee State University

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

Reference Format

1. C Caratheodory (1969). Conformal representation. Conformal representation
2. Z Nehari (1952). Conformal mapping. Conformal mapping
3. I Gradshteyn,I Ryzhik (1980). DETERMINANTS. Table of Integrals, Series, and Products, 1108-1113.
4. Dean Duffy (2001). Green's Functions with Applications. Green's Functions with Applications
5. R Haberman (2012). Applied Partial Differential Equations with Fourier Series and Boundary Value Problems. 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. J. Math. Anal. Appl, 344(1), 521-534.
7. Yuri Melnikov (2011). Infinite Products and Elementary Functions. Green's Functions and Infinite Products, 17-42.
8. P Morse,H Feshbach (1953). Methods of Theoretical Physics. Methods of Theoretical Physics, 2

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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. "Some Further Developments in the Infinite Product Representation of Elementary Functions". Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 13 (GJSFR Volume 13 Issue 14 (F4)).

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GJSFR Volume 13 Issue 14 (F4)

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

elementary functions green’s functions infinite products

Classification

GJSFR-F Classification MSC 2010: 08B25

26A09

Submission ReceivedMarch 17, 2013
Peer Review Double Blind
Handling Editor
Accepted April 14, 2013
Published March 29, 2013

Version of record

v1.2

Issue date

March 29, 2013

Language

English

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Article Matrices

Total Score: 131

Country: United States

Subject: Global Journal of Science Frontier Research - F: Mathematics & Decision

Authors: Viktor Reshniak (PhD/Dr. count: 0)

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Publish Date: 2013 03, Fri

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