Title: Exact series expansions, recurrence relations, properties and integrals of the generalized exponential integral functions
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.
Publication Year: 2006
Publication Date: 2006-10-03
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 7
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