A Harmonic Mean Inequality for the Exponential Integral Function

Nantomah, Kwara

doi:10.12732/ijam.v34i4.4

Cited by 3 publications

(3 citation statements)

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“…, Remark 2.11. Theorem 2.10 provides a far-reaching generalization of the results of the papers [8,9].…”

Section: Degenerate Exponential Integral Functionmentioning

confidence: 68%

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Degenerate exponential integral function and its properties

Nantomah¹

2022

AJMS

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PurposeIn 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.Design/methodology/approachThe methods adopted in establishing the results are theoretical in nature.FindingsA 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.Originality/valueThe results obtained in this paper are new and have the potential of inspiring further research on the subject.

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“…, Remark 2.11. Theorem 2.10 provides a far-reaching generalization of the results of the papers [8,9].…”

Section: Degenerate Exponential Integral Functionmentioning

confidence: 68%

“…For example see Refs. [3][4][5][6][7][8][9][10][11][12][13][14][15]. Among other things, Kim et al [16] defined the modified degenerate gamma function as…”

Section: Degenerate Exponential Integral Functionmentioning

confidence: 99%

Degenerate exponential integral function and its properties

Nantomah¹

2022

AJMS

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“…For similar results involving other special functions, one may refer to the works [14,15,16,17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Inequalities for Means Regarding the Trigamma Function

Nantomah,

Abe-I-Kpeng,

Sandow

2024

J. Nep. Math. Soc.

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Let G(α, β), A(α, β) and H(α, β), respectively, be the geometric mean, arithmetic mean and harmonic mean of α and β. In this paper, we prove that G(ψ′ (z), ψ′ (1/z)) ≥ π2/6, A(ψ′ (z), ψ′ (1/z)) ≥ π2/6 and H(ψ′ (z), ψ′ (1/z)) ≤ π2/6. This extends the previous results of Alzer and Jameson regarding the digamma function ψ. The mathematical tools used to prove the results include convexity, concavity and monotonicity properties of certain functions as well as the convolution theorem for Laplace transforms.

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