The object of the present paper is to investigate some inclusion relationships and a number of other useful properties of several subclasses of multivalent analytic functions, which are defined here by using the Dziok...
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The object of the present paper is to investigate some inclusion relationships and a number of other useful properties of several subclasses of multivalent analytic functions, which are defined here by using the Dziok-Srivastava operator. Relevant connections of the results presented here with those obtained in earlier works are pointed out. (c) 2007 Elsevier Ltd. All rights reserved.
We investigate the behaviour of the zeros of three distinct types of F-3(2) hypergeometric polynomials. Each type of polynomial considered has degree 2n and contains a free parameter b. We describe the location of the...
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We investigate the behaviour of the zeros of three distinct types of F-3(2) hypergeometric polynomials. Each type of polynomial considered has degree 2n and contains a free parameter b. We describe the location of the zeros as b varies continuously through rear values. Numerical tables of the zeros, generated by Mathematica, are presented in confirmation of our stated results. (C) 2001 Elsevier Science B.V. All rights reserved.
A summation formula is given for F-3(2)(a, b, c;1/2(a + b + i + 1), 2c + j;1) with fixed j and arbitrary i (i, j is an element of Z). This result generalizes the classical Watson's theorem which deals with the cas...
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A summation formula is given for F-3(2)(a, b, c;1/2(a + b + i + 1), 2c + j;1) with fixed j and arbitrary i (i, j is an element of Z). This result generalizes the classical Watson's theorem which deals with the case i = j = 0. Extensions to the cases of F-3(2)(a, 1 + i + j - a, c;e, 1 + i + 2c - e;1), and F-3(2)(a, b, c;1 + i + a - b, 1 + i + j + a - c;1) are given. Notice that the case i = j = 0 corresponds to the classical theorems due to Whipple and Dixon, respectively.
The 1888 paper by Salvatore Pincherle (Professor of Mathematics at the University of Bologna) on generalized hypergeometric functions is revisited. We point out the pioneering contribution of the Italian mathematician...
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The 1888 paper by Salvatore Pincherle (Professor of Mathematics at the University of Bologna) on generalized hypergeometric functions is revisited. We point out the pioneering contribution of the Italian mathematician towards the Mellin-Barnes integrals based on the duality principle between linear differential equations and linear difference equation with rational coefficients. By extending the original arguments used by Pincherle, we also show how to formally derive the linear differential equation and the Mellin-Barnes integral representation of the Meijer G functions. (C) 2002 Elsevier Science B.V. All rights reserved.
The possibility of extending to generalized hypergeometric functions a sum rule for confluent hypergeometricfunctions found by Temme is considered. (C) 2003 Elsevier B.V. All rights reserved.
The possibility of extending to generalized hypergeometric functions a sum rule for confluent hypergeometricfunctions found by Temme is considered. (C) 2003 Elsevier B.V. All rights reserved.
Recently many authors are spending lot of time and efforts to evaluate various operators of fractional order integration and differentiation and their generalizations of classes of, or particular, special functions. T...
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Recently many authors are spending lot of time and efforts to evaluate various operators of fractional order integration and differentiation and their generalizations of classes of, or particular, special functions. The list of such works is rather long and yet growing daily, so we limit ourselves to mention here only a few, just to illustrate our general approach. As special functions present indeed a great variety, and the operators of fractional calculus do as well, the mentioned job produces a huge flood of publications. Many of them use same formal and standard procedures, and besides, often the results sound not of practical use, with except to increase authors' publication activities. In this survey, we point out on some few basic classical results, combined with author's ideas and developments, that show how one can do the task at once, in the rather general case: for both operators of generalized fractional calculus and generalized hypergeometric functions. Thus, great part of the results in the mentioned publications are well predicted and fall just as special cases of the discussed general scheme. (C) 2017 Elsevier Ltd. All rights reserved.
In this paper, we derive hypergeometric function representation of one-loop contributing to Higgs decay to two photons in the standard model and its extensions. The calculations are performed at general space-time dim...
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In this paper, we derive hypergeometric function representation of one-loop contributing to Higgs decay to two photons in the standard model and its extensions. The calculations are performed at general space-time dimension d. For the first time, analytic results are published for form factors that are valid in arbitrary space-time dimension. Moreover, we confirm against analytic results in previous computations that have been available in space-time dimension d = 4 - 2 epsilon at epsilon(0) expansions.
Metal surface evolution is described by a nonlinear fourth-order partial differential equation for curvature-driven flow. The standard boundary conditions for grain-boundary grooving, at a grain-grain-fluid triple int...
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Metal surface evolution is described by a nonlinear fourth-order partial differential equation for curvature-driven flow. The standard boundary conditions for grain-boundary grooving, at a grain-grain-fluid triple intersection, involve a prescribed slope at the groove axis. The well-known similarity reduction is no longer valid when the dihedral angle and surface diffusivity depend on time due to variation of the surface temperature. We adapt a nonlinear fourth-order model that can be discerned from symmetry analysis to be integrable, equivalent to the fourth-order linear diffusion equation. The connection between classical symmetries and separation of variables allows us to develop the correction to the self-similar approximation as a power series in a time-like variable.
This paper begins by studying several properties and characteristics of certain subclasses of analytic functions with positive coefficients. The results investigated here include various coefficient inequalities, dist...
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This paper begins by studying several properties and characteristics of certain subclasses of analytic functions with positive coefficients. The results investigated here include various coefficient inequalities, distortion properties, and the radii of close-to-convexity. Inclusion theorems involving the Hardy space of analytic functions and the class of functions whose derivative has a positive real part are also investigated. Relationships between certain subclasses of analytic functions (involving fractional derivative operators) with negative coefficients and a certain generalized fractional integral operator are then studied. Various known or new special cases of our results are also pointed out. (C) 1999 Elsevier Science Ltd. All rights reserved.
The expansion of a large class of functions in series of linearly varying Laguerre polynomials, i.e., Laguerre polynomials whose parameters are linear functions of the degree, is found by means of the hypergeometric f...
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The expansion of a large class of functions in series of linearly varying Laguerre polynomials, i.e., Laguerre polynomials whose parameters are linear functions of the degree, is found by means of the hypergeometricfunctions approach. This expansion formula is then used to obtain the Brown-Carlitz generating function (which gives a characterization of the exponential function) and the connection formula for these polynomials. Finally, these results are employed to connect the bound states of the quantum-mechanical potentials of Morse and Poschl-Teller, which are frequently used to describe molecular systems. (C) 2002 Elsevier Science B.V. All rights reserved.
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