A Class of Generalized Gamma Functions

A Class of Generalized Gamma Functions

In this paper, we study the holomorphic function defined by the infinite product Γa,r(s) = ∏ n≥0(1 + 1 a+nr ) (1 + s a+nr ) which generalize Euler’s definition in the sense that Γ(s) = Γ1,1(s) s . We obtain analogues of the Gauss multiplication formula, complement formula for functions Γa,r(s). Laboratoire Gevrey de Mathématique Physique, Université de Bourgogne, Faculté des Sciences et Techniq...

An upper bound to the second Hankel functional for the class of gamma-starlike functions

‎The objective of this paper is to obtain an upper bound to the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$‎ ‎for the function $f$‎, ‎belonging to the class of Gamma-starlike functions‎, ‎using Toeplitz determinants‎. ‎The result presented here include‎ ‎two known results as their special cases‎.  

Human Observation Based Generalized Gamma Functions

This paper describes an accurate method to obtain the Tone Reproduction Curve (TRC) of display devices without using a measurement device. It is an improvement of an existing technique based on human observation, solving its problem of numerical instability and resulting in functions in log–log scale which correspond better to the nature of display devices. We demonstrate the effiency of our te...

New inequalities for a class of differentiable functions

In this paper, we use the Riemann-Liouville fractionalintegrals to establish some new integral inequalities related toChebyshev's functional in the case of two differentiable functions.

A Numerical Integration Method by Using Generalized Series of Functions