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Degenerate exponential integral function and its properties. (English) Zbl 07825290

Summary: In this paper, the author introduces a degenerate exponential integral function and further studies some of its analytical properties. The new function is a generalization of the classical exponential integral function and the properties established are analogous to those satisfied by the classical function.
The methods adopted in establishing the results are theoretical in nature.
A degenerate exponential integral function which is a generalization of the classical exponential integral function has been introduced and its properties investigated. Upon taking some limits, the established results reduce to results involving the classical exponential integral function.

MSC:

26D07 Inequalities involving other types of functions
26D20 Other analytical inequalities
33Bxx Elementary classical functions

Software:

DLMF
Full Text: DOI

References:

[1] Abramowitz M, Stegun AI. Handbook of mathematical functions with formulas, graphic and mathematical tables. New York: Dover Publications; 1965.
[2] Olver FWJ, Lozier DW, Boisvert RF, Clark CW (Eds). NIST handbook of mathematical functions. London: Cambridge University Press; 2010. · Zbl 1198.00002
[3] Barry DA, Parlange J-Y, Li L. Approximation for the exponential integral (Theis well function). J Hydrol. 2000; 227: 287-291.
[4] Bhandari PK, Bissu SK. On some inequalities involving Turan-type inequalities. Cogent Math. 2016; 3(1): 1130678. · Zbl 1426.26040
[5] Chiccoli C, Lorenzutta S, Maino G. Recent results for generalized exponential integrals. Computers Math Applic. 1990; 19(5): 21-29. · Zbl 0701.33001
[6] Conway JT. Indefinite integrals involving the exponential integral function. Integral Transforms Spec Funct. 2022; 33(1): 1-15. doi: 10.1080/10652469.2021.1893718. · Zbl 1494.34109
[7] Lin S-D, Chao Y-S, Srivastava HM. Some expansions of the exponential integral in series of the incomplete Gamma function. Appl Math Lett. 2005; 18: 513-520. · Zbl 1087.33001
[8] Nantomah K. A harmonic mean inequality for the exponential integral function. Int J Appl Math. 2021; 34(4): 647-652.
[9] Nantomah K. A harmonic mean inequality concerning the generalized exponential integral function. Adv Math Sci J. 2021; 10(9): 3227-3231.
[10] Nantomah K, Merovci F, Nasiru S. A generalization of the exponential integral and some associated inequalities. Honam Math J. 2017; 39(1): 49-59. · Zbl 1372.26020
[11] Salem A. A q-analogue of the exponential integral. Afr Mat. 2013; 24: 117-125. · Zbl 1353.41007
[12] Sroysang B. On the n-th derivative of the exponential integral functions. Commun Math Appl. 2013; 4(2): 141-144.
[13] Sulaiman WT. Turan inequalities for the exponential integral functions. Commun Optim Theory. 2012; 1(1): 35-41.
[14] Yakubu A, Nantomah K, Iddrisu MM. A p-analogue of the exponential integral function and some properties. Adv Inequal Appl. 2020; 2020: 1-9.
[15] Zenku T, Jolevska-Tuneska B, Tuneski N. Results on the exponential integral. Sarajevo J Math. 2017; 13(1): 71-80. · Zbl 1424.46060
[16] Kim Y, Kim BM, Jang L-C, Kwon J. A note on modified degenerate gamma and laplace transformation. Symmetry. 2018; 10(471): 1-8.
[17] Miller KS, Samko SG. Completely monotonic functions. Integr Transf and Spec Funct. 2001; 12(4): 1-15.
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