[PDF] Top 20 A CERTAIN CLASS OF MULTIPLE GENERATING FUNCTIONS INVOLVING MITTAG-LEFFLER S FUNCTIONS

... (3.7) Now putting α i = α = 1 and β i = λ i + 1 {i=1,2,…,n} and β=λ+1 and replacing z/n+1 by − z 2 / 4 and x i by x i 2 {i=1,2,…,n}, respectively, in (2.9) and using the relation (1.7), we get a multiple ... See full document

... integral involving the product of the extension of the generalized multiple-index Mittag-Leffler function, product of two Bessel functions and product of two the multivariable ... See full document

... integral involving the product of a generalized multiple-index Mittag-Leffler function,product of three Bessel functions, multivariable Aleph-function, the multivariable I-function ... See full document

... integral involving the product of a generalized multiple-index Mittag-Leffler function,trigonometric functions, multivariable Aleph-function, the multivariable I-function defined by ... See full document

... of multiple variables. The multiple Mellin-Barnes integral occuring in this paper will be referred to as the multivariables Aleph-function throughout our present study and will be defined and represented as ... See full document

... generalized multiple Zeta-function in multiple serie with the help of equation ...general class of polynomial of several variables with the help of equation ...of s variables in Mellin-Barnes ... See full document

... formulas involving the extended Mittag-Leffler function based on the well known Lavoie and Trot- tier integral formula and the obtain results are express in term of extended Wright-type ...establish ... See full document

... integral involving the generalized multiple-index Mittag-Leffler function, the hyperbolic functions, the multivariable Aleph-function, a class of polynomials of several variables ... See full document

... integral involving the g eneralized multiple-index Mittag-Leffler function , the product of Bessel's functions, the multivariable Aleph-function, a class of polynomials of ... See full document

... of multiple variables. The multiple Mellin-Barnes integrals occurring in this paper will be referred to as the multivariables Aleph-function throughout our present study and will be defined and represented ... See full document

... The class of typically real functions T was intro- duced by Robertson ...∈ S is said to be convex in the direction of imaginary axis if and only if the domain f (U ) is convex in the direction of ... See full document

... This is a survey paper on a part of author’s publications, referring to the dif- ferentiation and integration of an arbitrary order of the Bessel type functions. In the beginning we consider both the classical ... See full document

... The importance of fractional differential equations in the field of applied science has gained more attention not only in mathematics but also in dynamical systems, physics, control systems, and engineering, creating ... See full document

... The functions which are continuous but non-differentiable in integer order calculus can be characte- rized in terms of fractional calculus and especially through Holder exponent [10] ...differentiable ... See full document

... of Mittag-Leffler function ; its various properties including differentiation,Laplace ,Beta, and Mellin transforms,and generalized hypergeometric series form and its relationship with other type of special ... See full document

... relevant Mittag-Leffler ...of certain Mittag-Leffler functions have been used by [18] in their stability considerations of fractional differential ... See full document

... In this section of the present note, we have given some of our observations on the works 1.2 . At first, we would like to mention that the authors of the paper 1 perhaps fail to notice the work 4 in which the above ... See full document

... This is a soxnewhat general integral expansion formula for a function fz defined in Zl,Z2 where < x < 2 < l, which is perhaps useful in solving certain boundary value problems of mathema[r] ... See full document

... [1] M. Abramowitz and I. A. Stegun (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Reprint of the 1972 edition. A Wiley-Interscience Pub- lication. Selected Government ... See full document

... special functions of Mathematics Physics and their use in [4] Raizada ...special functions of Mathematics Physics and their use in statistical and boundary value ... See full document