Establishment of Order of 4-Tuples Concerning Familiar Polynomials with Captivating Condition

V Pandichelvi; B Umamaheswari

doi:10.17485/IJST/v16i36.1578

Article

Establishment of Order of 4-Tuples Concerning Familiar Polynomials with Captivating Condition

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i36.1578

Year: 2023, Volume: 16, Issue: 36, Pages: 2982-2987

Original Article

Establishment of Order of 4-Tuples Concerning Familiar Polynomials with Captivating Condition

V Pandichelvi¹, B Umamaheswari^2*

¹Assistant Professor, PG & Research Department of Mathematics, Urumu Dhanalakshmi College (Affiliated to Bharathidasan University), Trichy, Tamil Nadu, India
²Assistant Professor, Department of Mathematics, Meenakshi College of Engineering, Chennai, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:24 June 2023, Accepted Date:14 August 2023, Published Date:27 September 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: Finding the feature of a number pattern is a fascinating area of current research. There are numerous features, one of which is that the Area by Perimeter of a Pythagorean triangle is a nasty number, figurate number, and so on. This manuscript aims to identify the precise sorts of 4-tuples combining Legendre polynomials and Probabilist’s Hermite polynomials in which the product of any two polynomials is added by one square to another polynomial. Method: By using specific transformation, the assumption can be turned into a universal second-degree equation with two variables known as the Pell equation. The solution to this equation yields 3-tuples and their extension into 4-tuples from 2-tuples in a precise manner, as explained. Findings: This paper describes some types of 4-tuples involving Legendre polynomials and Probabilist’s Hermite polynomials in which the product of any two polynomials is added by the number one in any 4-tuple results in the square of an alternate polynomial. Novelty: A Python program is achieved for displaying all 4-tuples with the numerical values of the specified unknown combination with the special property.

Keywords: Legendre polynomials; Probabilist’s Hermite polynomials; Pell equation; Integer solutions; Diophantine m-tuples

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Copyright

© 2023 Pandichelvi & Umamaheswari. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)