Approximation of Planck distribution



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.


thermal radiation Planck function incomplete Riemann zeta function analytical approximation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 1 (McGraw-Hill, New York, 1953).Google Scholar
  2. 2.
    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
  3. 3.
    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

Personalised recommendations