Alternative Analytic and Friendly Solution of the Bose-Einstein Integral

9th Annual Basic Science International Conference 2019

自然科学（总论）

Juwono, Alamsyah M.^1 ; Istiroyah^1 ; Nuriyah, L.^1

Department of Physics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Malang, Indonesia^1

关键词: Analytic solution;    Black body radiation;    Bose-Einstein statistics;    Divergent series;    Mathematical relation;    Planck distribution;    Riemann zeta functions;    Special functions;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/546/5/052036/pdf
DOI  :  10.1088/1757-899X/546/5/052036

学科分类：自然科学（综合）

来源: IOP

【 摘 要 】

A study to find an analytic, and fairly friendly, solution of Bose-Einstein Integral has been conducted, by employing various common mathematical relations, mainly the Fourier Series. The result obtained was without approximation, and did not involve any divergent series. This study was carried out with motivation to obtain analytic solutions from Integral Bose-Einstein, which is very important in the study of Planck Distribution of blackbody radiation, and in Bose-Einstein statistic; and to show that the Bose-Einstein Integral can, in fact, be solved without involving complicated special functions. The Bose-Einstein Integral, surely, had been solved by large number of authors, generally, by utilizing various special functions, such as, by using the Riemann-Zeta function [1][2][6][7]. This study produced the same results as previously obtained through various ways, that is π 4 / 15, which guarantees that the steps we conducted were correct mathematically.