Generalized hypergeometric function

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Heat Conduction and Sequence of Functions Containing Generalized Hypergeometric Function

Heat Conduction and Sequence of Functions Containing Generalized Hypergeometric Function

The main aim of this paper is to obtain the solution of heat conduction partial differential equation pertaining to sequence of functions containing generalized hypergeometric function and the multivariable I- function defined by Prathima et. al. [ 7 ]. Some particular cases related to H- function of several variables and I- function of two variables given by Rathi et. al. [11 ] are mentioned.

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Selberg integral involving the incomplete generalized hypergeometric function,a class of polynomials and multivariable Aleph-functions

Selberg integral involving the incomplete generalized hypergeometric function,a class of polynomials and multivariable Aleph-functions

In the present paper we evaluate the modified Selberg integral involving the product of a multivariable Aleph-functions, a extension of the incomplete generalized hypergeometric function and general class of polynomials of several variables. The importance of the result established in this paper lies in the fact they involve the Aleph-function of several variables which is sufficiently general in nature and capable to yielding a large of results merely by specializating the parameters their in.We will study two particular cases.

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On general Eulerian integral of certain product Prasad's multivariable I-function, the classes of polynomials and generalized hypergeometric function

On general Eulerian integral of certain product Prasad's multivariable I-function, the classes of polynomials and generalized hypergeometric function

In this paper we have evaluated a generalized Eulerian integral involving the product of the multivariable I-function In this paper we have evaluated a generalized Eulerian integral involving the product of the multivariable I-function defined by Prasad [1], the classes of multivariable polynomials and generalized hypergeometric function with general defined by Prasad [1], the classes of multivariable polynomials and generalized hypergeometric function with general arguments. The formulae established in this paper is very general nature. Thus, the results established in this research arguments. The formulae established in this paper is very general nature. Thus, the results established in this research work would serve as a key formula from which, upon specializing the parameters, as many as desired results involving work would serve as a key formula from which, upon specializing the parameters, as many as desired results involving the special functions of one and several variables can be obtained.
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On general Eulerian integral of certain product of Kumari's multivariable I-function the classes of polynomials and generalized hypergeometric function

On general Eulerian integral of certain product of Kumari's multivariable I-function the classes of polynomials and generalized hypergeometric function

The object of this paper is to establish an general Eulerian integral involving the product of the multivariable I-function defined by Kumari et al [2], the general classes of multivariable polynomials and a generalized hypergeometric function which provide unification and extension of numerous results. We will study the particular case concerning the multivariable H-function defined by Srivastava et al [9] and the Srivastava-Daoust polynomial [6].

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On general Eulerian integral of certain product multivariable A-function, the classes of polynomials and generalized hypergeometric function

On general Eulerian integral of certain product multivariable A-function, the classes of polynomials and generalized hypergeometric function

The object of this paper is to establish an general Eulerian integral involving the product of the multivariable A-function defined by Gautam et al [1], the general classes of multivariable polynomials and a generalized hypergeometric function which provide unification and extension of numerous results. We will study the particular case concerning the multivariable H-function defined by Srivastava et al [8] and the Srivastava-Daoust polynomial [5].

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Certain Properties of Extended Wright Generalized Hypergeometric Function

Certain Properties of Extended Wright Generalized Hypergeometric Function

Abstract. In this paper, we obtain the extended Wright generalized Hypergeometric function using extended Beta function. We also obtain certain integral representations, Mellin transform and some derivative properties of extended Wright generalized Hypergeometric function. Further, we represent extended Wright generalized Hypergeometric function in the form of Laguerre polynomials and Whittaker function. Keywords: Extended Wright generalized Hypergeometric function; Extended Beta function; Laguerre polynomials; Whittaker function; Mellin transform; Fractional derivative operator
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On general Eulerian integral of certain product of multivariable Aleph-function, the classes of polynomials and generalized hypergeometric function

On general Eulerian integral of certain product of multivariable Aleph-function, the classes of polynomials and generalized hypergeometric function

To prove (3.14), first expressing a class of multivariable polynomials defined by Srivastava [4] in serie with the help of (1.13), a class of multivariable polynomials defined by Srivastava et al [6] in serie with the help of (1.14) and we interchange the order of summations and t-integral (which is permissible under the conditions stated). Expressing the Aleph-functions of r-variables in terms of Mellin-Barnes type contour integral with the help of (1.1)and the generalized hypergeometric function in Mellin-Barnes contour integral with the help of (2.1) and interchange the order of integrations which is justifiable due to absolute convergence of the integral
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Some properties of Wright type generalized hypergeometric function via fractional calculus

Some properties of Wright type generalized hypergeometric function via fractional calculus

This paper is devoted to the study of a Wright-type hypergeometric function (Virchenko, Kalla and Al-Zamel in Integral Transforms Spec. Funct. 12(1):89-100, 2001) by using a Riemann-Liouville type fractional integral, a differential operator and Lebesgue measurable real or complex-valued functions. The results obtained are useful in the theory of special functions where the Wright function occurs naturally. MSC: 33C20; 33E20; 26A33; 26A99

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Abstract The term "hypergeometric function" sometimes refers to the generalized hypergeometric function. In mathematics, the Gaussian or ordinary hypergeometric function

Abstract The term "hypergeometric function" sometimes refers to the generalized hypergeometric function. In mathematics, the Gaussian or ordinary hypergeometric function

The term "hypergeometric series" was first used by John Wallis in his 1655 book Arithmetica Infinitorum. Hypergeometric series were studied by Euler, but the first full systematic treatment was given by Gauss (1813), Studies in the nineteenth century included those of Ernst Kummer (1836), and the fundamental characterisation by Bernhard Riemann of the hypergeometric function by means of the differential equation it satisfies. Riemann showed that the second-order differential equation (in z) for the 2 F 1 , examined in
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8. Harmonic  univalent  Functions associated With
generalized hypergeometric functions

8. Harmonic univalent Functions associated With generalized hypergeometric functions

Abstract. The generalized hypergeometric function is used here to introduce a new class of complex valued harmonic functions which are orientation pre- serving and univalent in the open unit disc. Among the results presented in this paper include the coefficient bounds, distortion inequality and covering property, extreme points and certain inclusion results for this generalized class of functions.

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On Certain Class of Analytic Functions Related to Cho Kwon Srivastava Operator

On Certain Class of Analytic Functions Related to Cho Kwon Srivastava Operator

Kim, “Inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function,” Applied Mathematics and Computation, vol.. Srivastava, “I[r]

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The Application of Generalized Prolate Spheroidal Wave Function, Class of Multivariable Polynomials, and the Multivariable Gimel-Function in Heat Conduction

The Application of Generalized Prolate Spheroidal Wave Function, Class of Multivariable Polynomials, and the Multivariable Gimel-Function in Heat Conduction

Specializing the parameters of the multivariable Gimel-function, the generalized hypergeometric function and the multivariable polynomials, we can obtain a large number of results of problem of heat conduction involving various special functions of one and several variables useful in Mathematics analysis, Applied Mathematics, Physics and Mechanics. The result derived in this paper is of general character and may prove to be useful in several interesting situations appearing in the literature of sciences.

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Some subclasses of multivalent spirallike meromorphic functions

Some subclasses of multivalent spirallike meromorphic functions

Aouf, MK: Certain subclasses of meromorphically multivalent functions associated with generalized hypergeometric function.. Aouf, MK: Certain subclasses of meromorphically p-valent funct[r]

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Application of Special Functions in One Dimensional Advective Diffusion Problem

Application of Special Functions in One Dimensional Advective Diffusion Problem

In the present paper, we construct an one dimensional advective diffusion model problem to evaluate the substance concentration distribution along axis between and Here, the diffusivity of the substance and the velocity of the solvent flow are both considered as a variable. Kumar and Satyarth [6] use the product of the class of multivariable polynomials and the multivariable H-function defined here to obtain the analytic solution. Then, we employ the product of the generalized hypergeometric function, class of multivariable polynomials and the multivariable Gimel-function to obtain an analytic formula of our problem. Finally, some particular cases will be given.
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Sufficient Conditions for a New Class of Polynomial Analytic Functions of Reciprocal Order alpha

Sufficient Conditions for a New Class of Polynomial Analytic Functions of Reciprocal Order alpha

[13] Y. Sun, W. P. Kuang, Z. G. Wang, On meromorphic starlike functions of reciprocal order α, Bull. Malays. Math. Sci. Soc. (2) 35(2) (2012), 469–477. [14] Z. G. Wang, Y. P. Jiang, H. M. Srivastava, Some subclasses of meromorphi- cally multivalent functions associated with the generalized hypergeometric function, Comput. Math. Appl. 57(4) (2009), 571–586.

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Certain Results for a Subclass of Meromorphic Multivalent Functions Associated with the Wright Functions

Certain Results for a Subclass of Meromorphic Multivalent Functions Associated with the Wright Functions

In this paper, we introduce a new subclass of meromorphic multivalent functions associated with Wright generalized hypergeometric function and obtain new results for this class by the ap[r]

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6. A Class of Multivalent Analytic Functions with fixed Argument

6. A Class of Multivalent Analytic Functions with fixed Argument

Abstract. In this paper, a class of analytic functions with fixed argument of its coefficients involving Wright’s generalized hypergeometric function is defined with the help of subordination. The coefficient inequalities have been derived. Growth, distortion bounds and extreme points for functions belonging to the defined class have been investigated with consequent results.

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A Finite Single Integral Representation for the Polynomial Set Tn(x1,x2,x3,x4)

A Finite Single Integral Representation for the Polynomial Set Tn(x1,x2,x3,x4)

where (i = 1, 2, 3, 4) and      , 1 , 2 , 3 , 4 are real and m m m m m , 1 , 2 , 3 , 4 are positive integer. The left hand side of (1.1) contains the product of two generalized hypergeometric function which contains Appell function of four variables in the notation of Burchanall and Chaundy [1] associated with Lauricella function. The polynomial set contains a number of parameters for simplicity, itis denoted by T n (x

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Fractional Calculus Results Based On Extended Gauss Hypergeometric Functions and Via Pathway Model

Fractional Calculus Results Based On Extended Gauss Hypergeometric Functions and Via Pathway Model

We conclude this study by pointing out that the results obtained here are of a general nature and make it possible to extract multiple integrated formulas in the integrated pathway fractional integral. We have studied the fractional composition of the pathway fractional integral operator with a product extended generalized hypergeometric function. The results obtained here are useful for deriving many complementary integrator operators for each family of extended extended hypergeometric functions

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A Study of Unified Fractional Integral Operators Involving S-Generalized Gauss's Hypergeometric, Fox's H-Function and Gimel Function

A Study of Unified Fractional Integral Operators Involving S-Generalized Gauss's Hypergeometric, Fox's H-Function and Gimel Function

[7] H.M. Srivastava, M. Aslam Chaudhry and R. P. Agarwal, The incomplete Pochhammer symbols and their applications to hypergeometric and related functions, Integral Transforms and Special Functions: 23, 659683 (2012) [8] H. M. Srivastava, P. Agarwal and S. Jain, Generating functions for the generalized Gauss hypergeometric functions, Applied Mathematics and Computation 247, 348352 (2014).

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