Transformation of Special Relativity into Differential Equation by Means of Power Series Method
Chandra Bahadur Khadka

Chandra Bahadur Khadka, Department of Physics, Tri-Chandra Multiple Campus, Tribhuvan University, Kathmandu, Nepal. 

Manuscript received on 04 September 2023 | Revised Manuscript received on 12 September 2023 | Manuscript Accepted on 15 September 2023 | Manuscript published on 30 September 2023 | PP: 10-15 | Volume-10 Issue-1, September 2023 | Retrieval Number: 100.1/ijbsac.B1045103223 | DOI: 10.35940/ijbsac.B1045.0910123

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Abstract: Partial differential equations such as those involving Bessel differential function, Hermite’s polynomial, and Legendre polynomial are widely used during the separation of the wave equation in cylindrical and spherical coordinates. Such functions are quite applicable to solve the wide variety of physical problems in mathematical physics and quantum mechanics, but until now, there has been no differential equation capable for handling the problems involved in the realm of special relativity. In order to avert such trouble in physics, this article presents a new kind of differential equation of the form: , where c is the speed of light in a vacuum. In this work, the solution of this equation has been developed via the power series method, which generates a formula that is completely compatible with relativistic phenomena happening in nature. In this highly exciting topic, the particular purpose of this paper is to define entirely a new differential equation to handle physical problems happening in the realm of special relativity.

Keywords: Bessel Differential Equation, Hermite’s Polynomial, Legendre Polynomial, Mass Variation, Special Relativity, Time Dilation Etc.
Scope of the Article: Mathematical Physics