Monotonicity results and inequalities for the gamma and error functions

Supplements to Known Monotonicity Results and Inequalities for the Gamma and Incomplete Gamma Functions

In particular they proved that for x > 0 and α = 0 the function [Γ(1 + 1/x)]x decreases with x, while when α=1 the function x[Γ(1+1/x)]x increases.Moreover they also showed that the values α= 0 and α= 1, in the properties mentioned above, cannot be improved if x ∈ (0,+∞). In this paper we continue the investigation on the monotonicity properties for the gamma function proving, in Section 2, the...

Monotonicity and inequalities for the gamma function

Bounds for the Ratio of Two Gamma Functions: from Gautschi’s and Kershaw’s Inequalities to Complete Monotonicity

Abstract In the expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, the author looks back and analyses some inequalities, the complete monotonicity of several functions involving ratios of two gamma or q-gamma functions, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions, some new bounds for the ratio...

Monotonicity Results for the Gamma Function

The function [Γ(x+1)] 1/x x+1 is strictly decreasing on [1,∞), the function [Γ(x+1)]1/x √ x is strictly increasing on [2,∞), and the function [Γ(x+1)] 1/x √ x+1 is strictly increasing on [1,∞), respectively. From these, some inequalities, for example, the Minc-Sathre inequality, are deduced, and two open problems posed by the second author are solved partially.

developing a pattern based on speech acts and language functions for developing materials for the course “ the study of islamic texts translation”

هدف پژوهش حاضر ارائه ی الگویی بر اساس کنش گفتار و کارکرد زبان برای تدوین مطالب درس "بررسی آثار ترجمه شده ی اسلامی" می باشد. در الگوی جدید، جهت تدوین مطالب بهتر و جذاب تر، بر خلاف کتاب-های موجود، از مدل های سطوح گفتارِ آستین (1962)، گروه بندی عملکردهای گفتارِ سرل (1976) و کارکرد زبانیِ هالیدی (1978) بهره جسته شده است. برای این منظور، 57 آیه ی شریفه، به صورت تصادفی از بخش-های مختلف قرآن انتخاب گردید...