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

ALTAÇ, ZEKERİYA

doi:10.1016/j.jqsrt.2006.09.002

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

Atıf İçin Kopyala

ALTAÇ Z.

JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, cilt.104, sa.3, ss.310-325, 2007 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 104 Sayı: 3
Basım Tarihi: 2007
Doi Numarası: 10.1016/j.jqsrt.2006.09.002
Dergi Adı: JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.310-325
Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

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.