✦ LIBER ✦

A main inequality for several special functions

✍ Scribed by Mohammad Masjed-Jamei

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 385 KB
Volume: 60
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2010.06.007

No coin nor oath required. For personal study only.

✦ Synopsis

By using a recent generalization of the Cauchy-Schwarz inequality we obtain several new inequalities for some basic special functions such as beta and incomplete beta functions, gamma, polygamma and incomplete gamma functions, error functions, various kinds of Bessel functions, exponential integral functions, Gauss hypergeometric and confluent hypergeometric functions, elliptic integrals, moment generating functions and the Riemann zeta function. We also apply the generalized Cauchy-Schwarz inequality to some classical integral transforms. All these new inequalities obey the general form

in which p, q are real parameters and k(x) is a specific positive function.

📜 SIMILAR VOLUMES

An integral inequality for differentiabl

An integral inequality for differentiable functions of several variables

✍ Yu. G. Reshetnyak 📂 Article 📅 1985 🏛 SP MAIK Nauka/Interperiodica 🌐 English ⚖ 368 KB

Landau inequality for function of severa

Landau inequality for function of several variables

✍ V. G. Timofeev 📂 Article 📅 1985 🏛 SP MAIK Nauka/Interperiodica 🌐 English ⚖ 466 KB

Supplements to Known Inequalities for So

Supplements to Known Inequalities for Some Special Functions

✍ Carla Giordano; Andrea Laforgia; Josip Pečarić 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 106 KB

We establish some inequalities for the Bessel functions of the first kind J x Ž . Ž . and for the modified Bessel functions I x and K x . Some of these results are obtained using the method of Giordano and Laforgia which is based essentially on the arithmetic᎐geometric mean inequality. Other result

A new inequality for entire functions

✍ R.A Zalik 📂 Article 📅 1989 🏛 Elsevier Science 🌐 English ⚖ 131 KB

A new inequality for symmetric functions

✍ Gustave A. Efroymson; Blair Swartz; Burton Wendroff 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 792 KB

Let x, > 0, y, ) 0 for i = I,..., n; and let a,(x) be the elementary symmetric function of n variables given by a,(x) = C ,<rl<...<,,<n~r,...~r,.Definethepartial ordering x< y if a,(x) (a,(y), j= l,..., n. We show that x<y=-x"<y", 0 ( a < 1, where (x"), = x7 . We also give a necessary and sufficient

A sharp inequality for Sobolev functions

✍ Pedro M Girão 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 58 KB

Let N 5, a > 0, be a smooth bounded domain in We prove there exists an α 0 > 0 such that, for all u ∈ H 1 ( )