Date of Award
Master of Science
Master of Arts and Science
The importance of Bessel's Function in Mathematical Physics is indicated by their application to the modern solutions of problems in Wave-Theory, Elasticity, Hydrodynamics and Optics, The designation of Bessel's Functions as cylindrical function has its source in the use of these functions to express solutions of such physical problems as flow of heat or electricity in solid circular cylinder. However, the Bessel's Function first appeared in connection with the problem of the vibration of a heavy string suspended from one end. No method was given for determining the coefficients of the series. It was in problems connected with astronomy that the first completely successful application of Bessel's Functions occurred.
The major concern here will be to develop a series solution of Bessel's equation of a first and second kind for all realm. The development of a solution in integral form can be found without much difficulty, and it will prove profitable to produce that solution, much rigor as possible be maintained, it was necessary to The derivatives of Bessel's Functions In order that as prove several theorems, are important, and these derivatives will be developed in connection with the series solution.
Finally, the application used was chosen because of its familiarity. It will be solved in a general form and values will be inserted for a particular case.
Friedrich Wilhelm Bessel, the discoverer of Bessel's Function, was born at Minden, Germany in 178^. His father hoped that he would enter a career in commerce, but his inate interest in astronomy soon caused his father to abandon such ideas. In 1813, Bessel was summoned to Konigsberg to direct a new observatory. Without a doubt, he inaugurated the modern era of astronomy. Modern astronomy of precision is due to him. During his life, he wrote over 350 treatise.
A. D. Stewart
Prairie View Agricultural and Mechanical College
Rights© 2021 Prairie View A & M University
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Date of Digitization
John B Coleman Library
City of Publication
West, B. G. (1957). Bessel's Functions And Their Applications. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/731