On Bose-Einstein Functions

Clunie, J. G.

doi:10.1088/0370-1298/67/7/308

Cited by 20 publications

(10 citation statements)

References 5 publications

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“…Traditionally Fermi-Dirac and Bose-Einstein functions have been found from tables and power series expansions. The 1938 paper by McDougall and Stoner [10] gave extensive tables for fermions and there was a discussion of the corresponding functions for bosons by London [11], with series expansions given by Robinson [12] and generalized by Clunie [13]. A consolidated treatment of these functions is found in Pathria [14].…”

Section: Introductionmentioning

confidence: 99%

On the Chemical Potential of Ideal Fermi and Bose Gases

Cowan

2019

J Low Temp Phys

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Knowledge of the chemical potential is essential in application of the Fermi-Dirac and the Bose-Einstein distribution functions for the calculation of properties of quantum gases. We give expressions for the chemical potential of ideal Fermi and Bose gases in 1, 2 and 3 dimensions in terms of inverse polylogarithm functions. We provide Mathematica functions for these chemical potentials together with low-and hightemperature series expansions. In the 3d Bose case we give also expansions about T B. The Mathematica routines for the series allow calculation to arbitrary order.

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Section: Introductionmentioning

confidence: 99%

On the Chemical Potential of Ideal Fermi and Bose Gases

Cowan

2019

J Low Temp Phys

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“…This expression is discussed in Clunie [5] and Dingle [6], and it links the Bose-Einstein functions to the Fermi-Dirac functions. When ( ) = and = 1/2, the following expression is found:…”

Section: Journal Of Complex Analysis 5 the Functions Erfc(•) And Erfimentioning

confidence: 99%

“…This article introduces a general method for analytically evaluating the integrals given in (1) and (2) for various functions, ( ). The denominator of the integrands in (1) or (2) is exactly that found in the familiar Fermi-Dirac [2][3][4] or BoseEinstein integrals [5,6]. These integrals are often encountered in statistical and quantum statistical mechanics [7][8][9].…”

Section: Introductionmentioning

confidence: 96%

The Application of Real Convolution for Analytically Evaluating Fermi-Dirac-Type and Bose-Einstein-Type Integrals

Selvaggi

Selvaggi²

2018

Journal of Complex Analysis

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The Fermi-Dirac-type or Bose-Einstein-type integrals can be transformed into two convergent real-convolution integrals. The transformation simplifies the integration process and may ultimately produce a complete analytical solution without recourse to any mathematical approximations. The real-convolution integrals can either be directly integrated or be transformed into the Laplace Transform inversion integral in which case the full power of contour integration becomes available. Which method is employed is dependent upon the complexity of the real-convolution integral. A number of examples are introduced which will illustrate the efficacy of the analytical approach.

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“…denotes the Cauchy principal value of the analytically continued Bose-Einstein integral g σ (ζ) at the point x on the boundary [40]. Note that the Bose-Einstein integral g 0 (x), i.e., the case of σ = 0, is an exception.…”

Section: A Three-dimensional Hard-sphere Bose Gasesmentioning

confidence: 99%

The explicit expression of the fugacity for weakly interacting Bose and Fermi gases

Dai

Xie

2017

Journal of Mathematical Physics

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In this paper, we calculate the explicit expression for the fugacity for two-and three-dimensional weakly interacting Bose and Fermi gases from their equations of state in isochoric and isobaric processes, respectively, based on the mathematical result of the boundary problem of analytic functions -the homogeneous Riemann-Hilbert problem. We also discuss the Bose-Einstein condensation phase transition of three-dimensional hard-sphere Bose gases.

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On Bose-Einstein Functions

Cited by 20 publications

References 5 publications

On the Chemical Potential of Ideal Fermi and Bose Gases

On the Chemical Potential of Ideal Fermi and Bose Gases

The Application of Real Convolution for Analytically Evaluating Fermi-Dirac-Type and Bose-Einstein-Type Integrals

The explicit expression of the fugacity for weakly interacting Bose and Fermi gases

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