We introduce and study two subclasses ？_（[α_1]）（A, B, λ） and ？_（[α_1]）~＋ （A, B, λ） of meromorphic p-valent functions defined by certain linear operator involving the generalized hypergeometric function....We introduce and study two subclasses ？_（[α_1]）（A, B, λ） and ？_（[α_1]）~＋ （A, B, λ） of meromorphic p-valent functions defined by certain linear operator involving the generalized hypergeometric function. The main object is to investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses. We also derive many interesting results for the Hadamard products of functions belonging to the class ？_（[α_1]）~＋（α, β, γ, λ）.展开更多
In this study,we aim to explore a novel class of twenty-five double integrals involving generalized hypergeometric functions.These integrals take the form:_(3)F_(2)[∫_(0)^(1)∫_(0)^(1)y^(c)(1-x)^(c-1)(1-y)^(c-1)(1-xy...In this study,we aim to explore a novel class of twenty-five double integrals involving generalized hypergeometric functions.These integrals take the form:_(3)F_(2)[∫_(0)^(1)∫_(0)^(1)y^(c)(1-x)^(c-1)(1-y)^(c-1)(1-xy)^(1-2c)1/2(a+b+i+1),2c+j;4y(1-x)(1-y)/(1-xy)^(2)]dxdy for i,j=0,±1,±2.The results are derived using generalized versions of Watson’s summation theorem,as established in earlier work by Lavoie et al.Additionally,fifty integrals,split into two sets of twenty-five,are presented as special cases of our main findings,offering further insights into the structure of these integrals.展开更多
This paper is sequel to the authors paper [18]. By using the generalized Burchnall-Chaundy operator method, the authors are aiming at deriving certain decomposition formulas for some interesting special cases of Kampe...This paper is sequel to the authors paper [18]. By using the generalized Burchnall-Chaundy operator method, the authors are aiming at deriving certain decomposition formulas for some interesting special cases of Kampe de Feriets series of double hypergeometric series F;.展开更多
The main aim of this article is to obtain certain Laurent type hypergeometric generating relations. Using a general double series identity, Laurent type generating functions(in terms of Kampede Feriet double hypergeom...The main aim of this article is to obtain certain Laurent type hypergeometric generating relations. Using a general double series identity, Laurent type generating functions(in terms of Kampede Feriet double hypergeometric function) are derived. Some known results obtained by the method of Lie groups and Lie algebras, are also modified here as special cases.展开更多
The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-fun...The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-function, Appell function F3 and a general class of poly- nomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus. On account of the general nature of the Saigo-Maeda operators, R-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notably H-function, /-function, Mittag-Leffier function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.展开更多
Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds t...Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.展开更多
In this paper, the displacement solution method of the conical shell is presented. From the differential equations in displacement form of conical shell and by introducing a displacement function, U,the differential e...In this paper, the displacement solution method of the conical shell is presented. From the differential equations in displacement form of conical shell and by introducing a displacement function, U,the differential equations are changed into an eight-order soluble partial differential equation about the displacement Junction U in which the coefficients are variable. A t the same time, the expressions of the displacement and internal force components of the shell are also given by the displacement function. As special cases of this paper, the displacement function introduced by V. Z. Vlasov in circular cylindrical shell, the basic equation of the cylindrical shell and that of the circular plate are directly derived.Under the arbitrary loads and boundary conditions, the general bending problem of the conical shell is reduced to finding the displacement functionU,and the general solution of the governing equation is obtained in generalized hypergeometric function, For the axisymmetric bending deformation of the conical shell, the general solution is expressed in the Bessel functionOn the basis of the governing equation obtained in this paper, the differential equation of conical shell on the elastic foundation (A Winkler Medium) is deduced, its general solutions are given in a power series, and the numerical calculations are carried out.展开更多
The aim of the present paper is to investigate some sufficient conditions for starlikeness and convexity of two new operatorsεα,λ^γand Hm^l(α1)related to the generalized Mittag-Leffler function Eα,λ^γand the g...The aim of the present paper is to investigate some sufficient conditions for starlikeness and convexity of two new operatorsεα,λ^γand Hm^l(α1)related to the generalized Mittag-Leffler function Eα,λ^γand the generalized hypergeometric function,defined in the unit disk,respectively.The results presented here make connections to some of the earlier known developments.展开更多
文摘We introduce and study two subclasses ？_（[α_1]）（A, B, λ） and ？_（[α_1]）~＋ （A, B, λ） of meromorphic p-valent functions defined by certain linear operator involving the generalized hypergeometric function. The main object is to investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses. We also derive many interesting results for the Hadamard products of functions belonging to the class ？_（[α_1]）~＋（α, β, γ, λ）.
基金Deanship of Scientific Research at Majmaah University for supporting this work under Project number(ICR-2023-622).
文摘In this study,we aim to explore a novel class of twenty-five double integrals involving generalized hypergeometric functions.These integrals take the form:_(3)F_(2)[∫_(0)^(1)∫_(0)^(1)y^(c)(1-x)^(c-1)(1-y)^(c-1)(1-xy)^(1-2c)1/2(a+b+i+1),2c+j;4y(1-x)(1-y)/(1-xy)^(2)]dxdy for i,j=0,±1,±2.The results are derived using generalized versions of Watson’s summation theorem,as established in earlier work by Lavoie et al.Additionally,fifty integrals,split into two sets of twenty-five,are presented as special cases of our main findings,offering further insights into the structure of these integrals.
文摘This paper is sequel to the authors paper [18]. By using the generalized Burchnall-Chaundy operator method, the authors are aiming at deriving certain decomposition formulas for some interesting special cases of Kampe de Feriets series of double hypergeometric series F;.
基金Dr.D.S.Kothari Post Doctoral Fellowship(Award letter No.F.4-2/2006(BSR)/MA/17-18/0025)awarded to Dr.Mahvish Ali by the University Grants CommissionGovernment of India,New Delhi。
文摘The main aim of this article is to obtain certain Laurent type hypergeometric generating relations. Using a general double series identity, Laurent type generating functions(in terms of Kampede Feriet double hypergeometric function) are derived. Some known results obtained by the method of Lie groups and Lie algebras, are also modified here as special cases.
基金NBHM Department of Atomic Energy,Government of India,Mumbai for the finanicai assistance under PDF sanction no.2/40(37)/2014/R&D-II/14131
文摘The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-function, Appell function F3 and a general class of poly- nomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus. On account of the general nature of the Saigo-Maeda operators, R-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notably H-function, /-function, Mittag-Leffier function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.
文摘Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.
文摘In this paper, the displacement solution method of the conical shell is presented. From the differential equations in displacement form of conical shell and by introducing a displacement function, U,the differential equations are changed into an eight-order soluble partial differential equation about the displacement Junction U in which the coefficients are variable. A t the same time, the expressions of the displacement and internal force components of the shell are also given by the displacement function. As special cases of this paper, the displacement function introduced by V. Z. Vlasov in circular cylindrical shell, the basic equation of the cylindrical shell and that of the circular plate are directly derived.Under the arbitrary loads and boundary conditions, the general bending problem of the conical shell is reduced to finding the displacement functionU,and the general solution of the governing equation is obtained in generalized hypergeometric function, For the axisymmetric bending deformation of the conical shell, the general solution is expressed in the Bessel functionOn the basis of the governing equation obtained in this paper, the differential equation of conical shell on the elastic foundation (A Winkler Medium) is deduced, its general solutions are given in a power series, and the numerical calculations are carried out.
基金the Youth Science Fund Research Project of Pingxiang University(Grant Nos.2019D0202,2018D0218,2018D0208)the Youth Fund Project of Science and Technology Research Project of Jiangxi Provincial Department of Education(Grant No.GJJ191157)。
文摘The aim of the present paper is to investigate some sufficient conditions for starlikeness and convexity of two new operatorsεα,λ^γand Hm^l(α1)related to the generalized Mittag-Leffler function Eα,λ^γand the generalized hypergeometric function,defined in the unit disk,respectively.The results presented here make connections to some of the earlier known developments.
