Abstract
In this paper uniform convergences of the two-dimensional exponential integral functions are investigated. We also study the continuity, integrability and asymptotic behaviour of these functions.
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Smith M.G.: The transport equation with plane symmetry and isotropic scattering. Proc. Cambridge Philos. Soc. 60, 909–920 (1964)
Hunt G.E.: The transport equation of radiative transfer with axial symmetry. SIAM J. Appl. Math. 16, 228–237 (1968)
Rybicki G.B.: The searchlight problem with isotropic scattering. JQSRT 11, 827–849 (1971)
Breig W.F., Crosbie A.L.: Two-dimensional radiative equilibrium. J. Math. Anal. Appl. 46, 104–125 (1974)
Breig W.F., Crosbie A.L.: Two-dimensional radiative equilibrium semi-infinite medium subjected to cosine varying radiation. JQSRT 13, 1395–1419 (1973)
Crosbie A.L., Koewing J.W.: Two-dimensional isotropic scattering. J. Math. Anal. Appl. 57, 91–109 (1977)
Crosbie A.L., Dougherty R.L.: Two-dimensional in a cylindrical geometry with anisotropic scattering. JQSRT 25, 551–569 (1981)
Crosbie A.L., Lee L.C.: Relation between multidimensional radiative transfer in cylindrical and rectangular coordinates with anisotropic scattering. JQSRT 38, 231–241 (1987)
Crosbie A.L., Lee L.C.: Multidimensional radiative transfer: a single integral represantation of anisotropic scattering kernels. JQSRT 42, 239–246 (1989)
Chapman S.: The absorption and dissociative or ionizing effect of monochromatic radiation in an atmosphere on a rotating earts. Proc. Phys. Soc. 43, 483–501 (1931)
Breig W.F., Crosbie A.L.: Numerical computation of a generalized exponential integral function. Math. Comput. 28, 575–579 (1974)
Prabha R.H., Yadav R.D.S.: Polynomial expressions for Bickley and exponential integral functions. Ann. Nucl. Energy 23, 1021–1025 (1996)
Humbert L., Vale V., Cottron M.: Experimental determination and emprical represantation of out-of-plane displacements in a cracked elastic plate loaded in mode I. Int. J. Solids Struct. 37, 5493–5504 (2000)
Guseinov I.I., Mamedov B.A.: On the evalution of generalized exponential integral functions. JQSRT 102, 251–256 (2006)
Guseinov I.I., Mamedov B.A.: Evalution of overlap integrals with integer and noninteger n Slater type orbitals using auxiliary functions. J. Mol. Model 8, 272–276 (2002)
Gradshteyn I.S., Ryzhik I.M.: Table of integrals, seriesand products. Academic Press, New York (2007)
I.M. Busbridge, The mathematics of radiative transfer. Cambridge (1960)
Chandrasekhar S.: Radiative Transfer. Dover Publications, New York (1960)
Sobelev V.V.: A Treatise on Radiative Transfer. Princeton, New York (1963)
Kourganoff V.: Basic Methods in Transfer Problems. Dover Publications, New York (1963)
Van de Hulst H.C.: Multiple Light Scattering, vol. 1. Academic Press, New York (1980)
Dance D.R., Day G.J.: Escape probabilities for fluorescent x-rays. Phys. Med. Biol. 30, 259–262 (1985)
Sharaf M.A.: General integral transform of the exponential integrals. Astrophys. Space Sci. 63, 295–314 (1979)
Thynell S.T., Ozisik M.N.: Integrals involving an exponential integral function and exponential arising in the solution of radiation transfer. JQSRT 33, 259–266 (1985)
Guseinov I.I., Mamedov B.A.: Use of analytical relations in evalution of exponential integral functions. J. Math. Chem. 38, 311–314 (2005)
Mamedov B.A., Merdan Z., Askerov I.M.: Evalution of exponential integrals using multinomial expansion theorems. J. Math. Chem. 38, 695–700 (2005)
Nikolsky S.M.: Course of Mathematical Analysis, vol. 2. Mir Publishers, Moscow (1977)
Prudnikov A.P., Brychkov Y.A., Marichev O.I.: Integrals and Series, vol. 3. Gordon and Breach, New York (1990)
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Aygar, Y., Bairamov, E. Properties of the two-dimensional exponential integral functions. J Math Chem 49, 1014–1025 (2011). https://doi.org/10.1007/s10910-010-9793-0
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DOI: https://doi.org/10.1007/s10910-010-9793-0