Exact series expansions, recurrence relations, properties and integrals of the generalized exponential integral functions


ALTAÇ Z.

JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, vol.104, no.3, pp.310-325, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 104 Issue: 3
  • Publication Date: 2007
  • Doi Number: 10.1016/j.jqsrt.2006.09.002
  • Title of Journal : JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER
  • Page Numbers: pp.310-325

Abstract

Generalized exponential integral functions (GEIF) are encountered in multi-dimensional thermal radiative transfer problems in the integral equation kernels. Several series expansions for the first-order generalized exponential integral function, along with a series expansion for the general nth order GEIF, are derived. The convergence issues of these series expansions are investigated numerically as well as theoretically, and a recurrence relation which does not require derivatives of the GEIF is developed. The exact series expansions of the two dimensional cylindrical and/or two-dimensional planar integral kernels as well as their spatial moments have been explicitly derived and compared with numerical values. (c) 2006 Elsevier Ltd. All rights reserved.