Inequalities involving the multiple psi function

Das, Sourav

doi:10.1016/j.crma.2018.01.014

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Cited by 2 publications

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“…Let m ≥ n be any natural number. Then taking logarithm on both sides of (2) and differentiating m + 1 times, we have (see also [8])…”

Section: Resultsmentioning

confidence: 99%

A complete monotonicity property of the multiple gamma function

Das¹

2020

Comptes Rendus. Mathématique

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We consider the following functions f n (x) = 1 − ln x + lnG n (x + 1) x and g n (x) = x G n (x + 1) x , x ∈ (0, ∞), n ∈ N, where G n (z) = (Γ n (z)) (−1) n−1 and Γ n is the multiple gamma function of order n. In this work, our aim is to establish that f (2n) 2n (x) and (ln g 2n (x)) (2n) are strictly completely monotonic on the positive half line for any positive integer n. In particular, we show that f 2 (x) and g 2 (x) are strictly completely monotonic and strictly logarithmically completely monotonic respectively on (0, 3]. As application, we obtain new bounds for the Barnes G-function.

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“…Let m ≥ n be any natural number. Then taking logarithm on both sides of (2) and differentiating m + 1 times, we have (see also [8])…”

Section: Resultsmentioning

confidence: 99%

A complete monotonicity property of the multiple gamma function

Das¹

2020

Comptes Rendus. Mathématique

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New asymptotic expansions and Padé approximants related to the triple gamma function

Das

Swaminathan

2022

J Inequal Appl

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In this work, our main focus is to establish asymptotic expansions for the triple gamma function in terms of the triple Bernoulli polynomials. As application, an asymptotic expansion for hyperfactorial function is also obtained. Furthermore, using these asymptotic expansions, Padé approximants related to the triple gamma function are derived as a consequence. The results obtained are new, and their importance is demonstrated by deducing several interesting remarks and corollaries.

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Inequalities involving the multiple psi function

Cited by 2 publications

References 14 publications

A complete monotonicity property of the multiple gamma function

A complete monotonicity property of the multiple gamma function

New asymptotic expansions and Padé approximants related to the triple gamma function

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