Analytical computation of Bose-Einstein integral functions

  • Akbari Jahan Department of Physics, North Eastern Regional Institute of Science and Technology Nirjuli – 791109 Arunachal Pradesh, India
Keywords: Bose-Einstein integral function, Gamma function, Riemann zeta function, Lanczos approximation, Gauss-Laguerre Quadrature.

Abstract

The study of Bose-Einstein integral functions is important in the fact that such functions arise in various numerical calculations of different domains of physics. The significance of gamma function and Riemann zeta function in solving such integrals has been studied and functional equations are evaluated thereby enabling the integrals of all orders to be calculated.

Downloads

Download data is not yet available.

References

[1] R. B. Dingle, ”The Bose-Einstein Integrals Bp(η) = (p!)−1 R ∞ 0 p (e−η − 1)−1 d”, Applied Scientific Research, Section A 6, 240 (1957).
[2] H. E. Haber and H. A. Weldon, ”On the relativistic Bose-Einstein integrals”, J. Math. Phys. 23, 1852 (1982).
[3] W. Gautschi, ”On the computation of generalized Fermi-Dirac and BoseEinstein integrals”, Comput. Phys. Commun. 74, 233 (1993).
[4] V. Bhagat, R. Bhattacharya and D. Roy, ”On the evaluation of generalized Bose-Einstein and Fermi-Dirac integrals”, Comput. Phys. Commun. 155, 7 (2003).
[5] A. Tassaddiq and A. Qadir, ”Fourier Transform Representation of the Extended Fermi-Dirac and Bose-Einstein Functions with Applications to the family of the zeta and related functions”, arXiv:1104.4346[math-ph]
[6] J. P. Selvaggi and J. A. Selvaggi, ”The Application of Real Convolution for analytically evaluating Fermi-Dirac-type and Bose-Einstein-type integrals”, J. Complex Analysis 2018, Article ID 5941485 (2018).
[7] E. Babolian and A. Arzhang Hajikandi, ”Numerical computation of the Riemann zeta function and prime counting function by using Gauss-Hermite and Gauss-Laguerre quadratures”, Int. J. Comput. Mathematics 87, 3420 (2010).
[8] A. Laurincikas, ”One transformation formula related to the Riemann zetafunction”, Integral Transforms and Special Functions 19, 577 (2008).
[9] F. London, ”On the Bose-Einstein Condensation”, Phys. Rev. 54, 947 (1938).
[10] F. London, ”The State of Liquid Helium near Absolute Zero”, J. Phys. Chem. 43, 49 (1939).
[11] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (New York: Dover) (1972).
[12] E. Kreyszig, Advanced Engineering Mathematics (New York: Wiley) (2010).
[13] E. C. Titchmarsh, The Theory of the Riemann Zeta Function (New York: Clarendon Press) (1987).
[14] C. Lanczos, ”A Precision Approximation of the Gamma Function”, J. SIAM Numer. Anal. Ser. B 1, 86 (1964).
[15] R. Ayoub, ”Euler and the Zeta Function”, Amer. Math. Monthly 81, 1067 (1974).
[16] J. E. Robinson, ”Note on the Bose-Einstein Integral Functions”, Phys. Rev. 83, 678 (1951).
[17] G. B. Arfken, H. J. Weber and F. E. Harris, Mathematical Methods for Physicists (Academic Press) (2012).
Published
2021-01-19
How to Cite
Jahan, A. (2021). Analytical computation of Bose-Einstein integral functions. Boson Journal of Modern Physics, 8(1), 1-9. Retrieved from http://scitecresearch.com/journals/index.php/bjmp/article/view/1952
Section
Articles