On the computation of Debye functions of integer orders

Ng, Edward W.; Devine, C. J.

doi:10.1090/s0025-5718-1970-0272160-6

Cited by 5 publications

(1 citation statement)

References 7 publications

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“…Therefore, some combination of numerical methods, expansions [8,9], and limiting expressions are required to evaluate flux. As regards numerical methods, numerically integrating the Bose-Einstein integral is time consuming and, without due care, prone to error.…”

Section: Introductionmentioning

confidence: 99%

Rapid and precise calculations of energy and particle flux for detailed-balance photovoltaic applications

Levy

Honsberg

2006

Solid-State Electronics

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Section: Introductionmentioning

confidence: 99%

Rapid and precise calculations of energy and particle flux for detailed-balance photovoltaic applications

Levy

Honsberg

2006

Solid-State Electronics

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Analysis of tandem solar cell efficiencies under AM1.5G spectrum using a rapid flux calculation method

Bremner

Levy

Honsberg

2007

Progress in Photovoltaics

273

200

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We report the use of a rapid flux calculation method using incomplete Riemann zeta functions as a replacement for the Bose–Einstein integral in detailed balance calculations to study the efficiency of tandem solar cell stacks under the terrestrial AM1.5G spectrum and under maximum concentration. The maximum limiting efficiency for unconstrained and constrained tandem stacks of up to eight solar cells, under the AM1.5G spectrum and maximum concentration, are presented. The results found agree well with previously published results with one exception highlighting the precautions necessary when calculating for devices under the AM1.5G spectrum. The band gap sensitivities of two tandem solar cell stack arrangements of current interest were also assessed. In the case of a three solar cell tandem stack the results show a large design space and illustrate that the constrained case is more sensitive to band gap variations. Finally, the effect of a non‐optimum uppermost band gap in a series constrained five solar cell tandem stack was investigated. The results indicate that a significant re‐design is only required when the uppermost band gap is greater than the optimum value with a relatively small effect on the limiting efficiency. It is concluded that this rapid flux calculation method is a powerful tool for the analysis of tandem solar cells and is particularly useful for the design of devices where optimum band gaps may not be available. Copyright © 2007 John Wiley & Sons, Ltd.

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Complex zeros of two incomplete Riemann zeta functions

Kölbig¹

1972

Math. Comp.

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Abstract. The computation of the complex zeros of an incomplete Riemann zeta function defined in an earlier paper is extended and new zero trajectories are given. A second incomplete Riemann zeta function is denned and its zero trajectories are investigated numerically as functions of the upper limit X of the definition integral. It becomes apparent that there exist three different classes of zero trajectories for this function, distinguished by their behaviour for X -► <*>.

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On the computation of Debye functions of integer orders

Abstract: An efficient method is presented for the computation of Debye functions of integer orders to twenty significant decimal digits.

Cited by 5 publications

References 7 publications

Rapid and precise calculations of energy and particle flux for detailed-balance photovoltaic applications

Rapid and precise calculations of energy and particle flux for detailed-balance photovoltaic applications

Analysis of tandem solar cell efficiencies under AM1.5G spectrum using a rapid flux calculation method

Complex zeros of two incomplete Riemann zeta functions

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