Approximation of Planck distribution

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Abstract

Calculation of thermal radiation transport frequently requires calculating the integral of the Planck distribution density with respect to a finite interval of spectrum. An analytical approximation of this integral and its related integrals in elementary functions is constructed.

Keywords

thermal radiation Planck function incomplete Riemann zeta function analytical approximation 

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References

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    H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 1 (McGraw-Hill, New York, 1953).Google Scholar
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    I. L. Tsvetkova and A. V. Shilkov, Implementation of the Method of Lebesgue Averaging of the Radiation Transport Equation, Preprint (Keldysh Institute of Applied Mathematics, Moscow, 1989).Google Scholar
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    B. N. Chetverushkin, Mathematical Simulation of Radiating Gas Dynamic Problems (Nauka, Moscow, 1985) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia

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