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Nous montrons que pour tout rationnel $α$ de $[- 1, 1]$ , l’ensemble des valeurs des polylogarithmes $\{{Li}_{s} (α), s \in ℕ, s \geq 1\}$ contient une infinité de nombres $ℚ$ -linéairement indépendants.

Inequalities and Asymptotic Formulae for the Three Parametric Mittag-Leffler Functions

Paneva-Konovska, Jordanka (2012)

Mathematica Balkanica New Series

MSC 2010: 33E12, 30A10, 30D15, 30E15We consider some families of 3-index generalizations of the classical Mittag-Le²er functions and study the behaviour of these functions in domains of the complex plane. First, some inequalities in the complex plane and on its compact subsets are obtained. We also prove an asymptotic formula for the case of "large" values of the indices of these functions. Similar results have also been obtained by the author for the classical Bessel functions and their Wright's...

Inequalities and identities for ... .

Dieter K. Ross (1980)

Aequationes mathematicae

Inequalities and monotonicity for the ratio of $Γ_{p}$ functions.

Krasniqi, Valmir, Merovci, Faton (2010)

International Journal of Open Problems in Computer Science and Mathematics. IJOPCM

Inequalities associating hypergeometric functions with planar harmonic mappings.

Ahuja, Om P., Silverman, H. (2004)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Inequalities for $3 - log$ -convex functions.

Chen, Donghui, Berenhaut, Kenneth S. (2008)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Inequalities for Beta and Gamma functions via some classical and new integral inequalities.

Dragomir, S.S., Agarwal, R.P., Barnett, N.S. (2000)

Journal of Inequalities and Applications [electronic only]

Inequalities for elliptic integrals.

Anderson, G.D., Vamanamurthy, M.K. (1985)

Publications de l'Institut Mathématique. Nouvelle Série

Inequalities for hyperbolic functions and their applications.

Zhu, L. (2010)

Journal of Inequalities and Applications [electronic only]

Inequalities for Laguerre functions.

Love, E.R. (1997)

Journal of Inequalities and Applications [electronic only]

Inequalities for logarithmic and exponential functions.

Constantinescu, Eugen (2004)

General Mathematics

Inequalities for power-exponential functions.

Qi, Feng, Debnath, Lokenath (2000)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Inequalities for some Whittaker functions

Lee Lorch (1967)

Archivum Mathematicum

Inequalities for Taylor series involving the divisor function

Horst Alzer, Man Kam Kwong (2022)

Czechoslovak Mathematical Journal

Let $T (q) = \sum_{k = 1}^{\infty} d (k) q^{k}, | q | < 1,$ where $d (k)$ denotes the number of positive divisors of the natural number $k$ . We present monotonicity properties of functions defined in terms of $T$ . More specifically, we prove that $H (q) = T (q) - \frac{log (1 - q)}{log (q)}$ is strictly increasing on $(0, 1)$ , while $F (q) = \frac{1 - q}{q} H (q)$ is strictly decreasing on $(0, 1)$ . These results are then applied to obtain various inequalities, one of which states that the double inequality $α \frac{q}{1 - q} + \frac{log (1 - q)}{log (q)} < T (q) < β \frac{q}{1 - q} + \frac{log (1 - q)}{log (q)}, 0 < q < 1,$ holds with the best possible constant factors $α = γ$ and $β = 1$ . Here, $γ$ denotes Euler’s constant. This refines a result of Salem, who proved the inequalities...

Inequalities for the gamma function.

Li, Xin, Chen, Chao-Ping (2007)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Inequalities for the smallest zeros of Laguerre polynomials and their $q$ -analogues.

Gupta, Dharma P., Muldoon, Martin E. (2007)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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