The asymptotic expansion of the generalized hypergeometric function F-p(q)(z) as z -> +infinity involves a coefficient sequence {c(k)}. Explicit formulas are given for this sequence when 0 <= (p) < (q). The r...
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The asymptotic expansion of the generalized hypergeometric function F-p(q)(z) as z -> +infinity involves a coefficient sequence {c(k)}. Explicit formulas are given for this sequence when 0 <= (p) < (q). The result is based on an integral representation of the generalized hypergeometric function that allows application of Watson's lemma.
The aim of this research paper is to evaluate filly double integrals involving a generalized hypergeometric function (25 each) in the form of [GRAPHICS] . in the most general form for any l is an element of Z and i, j...
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The aim of this research paper is to evaluate filly double integrals involving a generalized hypergeometric function (25 each) in the form of [GRAPHICS] . in the most general form for any l is an element of Z and i, j = 0, +/-1, +/-2. The results are derived with the help of generalization of Edwards's well known double integral due to Kim, et- al. and generalized classical Watson's summation theorem obtained earlier by Lavoie, et al. More than *** ine wresting special cases have also been obtained.
The paper studies logarithmic convexity and concavity of the generalized hypergeometric function with respect to the simultaneous shift of several parameters. We use integral representations and properties of Meijer&#...
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The paper studies logarithmic convexity and concavity of the generalized hypergeometric function with respect to the simultaneous shift of several parameters. We use integral representations and properties of Meijer's G function to prove log-convexity. When all parameters are shifted we use series manipulations to examine the power series coefficients of the generalized Turanian formed by the generalized hypergeometric function. In cases when all zeros of the generalized hypergeometric function are real, we further explore the consequences of the extended Laguerre inequalities and formulate a conjecture about reality of zeros.
In this paper, the parameter derivatives to any order of the generalized hypergeometric function as well as for its various special cases are obtained.
In this paper, the parameter derivatives to any order of the generalized hypergeometric function as well as for its various special cases are obtained.
A reduction formula for a generalizedhypergeometric F-p(p) as the product of an exponential and a polynomial is considered. The explicit formula for p = 1 given in the literature in terms of Laguerre polynomials is e...
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A reduction formula for a generalizedhypergeometric F-p(p) as the product of an exponential and a polynomial is considered. The explicit formula for p = 1 given in the literature in terms of Laguerre polynomials is extended to the case p = 2. As a by-product, a reduction formula for another F-2(2) hypergeometricfunction is given, and also for a Kampe de Feriet function.
作者：
Nemoto, YusukeChiba Univ
Grad Sch Sci Dept Math & Informat Yayoicho 1-33 Inage Chiba 2638522 Japan
In this paper, we express special values of the L-functions of certain CM elliptic curves which are related to Fermat curves in terms of the special values of generalized hypergeometric functions by comparing Bloch...
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In this paper, we express special values of the L-functions of certain CM elliptic curves which are related to Fermat curves in terms of the special values of generalized hypergeometric functions by comparing Bloch's element with Ross's element in the motivic cohomology group.
This paper is devoted to the study of a Wright-type hypergeometricfunction (Virchenko, Kalla and Al-Zamel in Integral Transforms Spec. Funct. 12(1): 89-100, 2001) by using a Riemann-Liouville type fractional integral...
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This paper is devoted to the study of a Wright-type hypergeometricfunction (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.
In this work, generalized hypergeometric functions for a bicomplex argument are introduced and the convergence criteria are derived. Furthermore, an integral representation of these functions is established. Moreover,...
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In this work, generalized hypergeometric functions for a bicomplex argument are introduced and the convergence criteria are derived. Furthermore, an integral representation of these functions is established. Moreover, quadratic transformation, a differential relation, analyticity, and contiguous relations of these functions are derived. Additionally, applications in quantum information systems and quantum optics are provided as a consequence. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
The classical hypergeometric summation theorems have a significant role in the theory of generalized hypergeometric functions. Over the years generalization and extension of classical summation theorems for the series...
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Virchenko and Rumiantseva [On the generalized associated legendre functions. Fract Cal Appl Anal. 2008;11(2): 175- 185] gave another generalization F-2(1)tau,beta(a, b;c;z) of the hypergeometricfunction. In this pape...
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Virchenko and Rumiantseva [On the generalized associated legendre functions. Fract Cal Appl Anal. 2008;11(2): 175- 185] gave another generalization F-2(1)tau,beta(a, b;c;z) of the hypergeometricfunction. In this paper, we give integral representations and differentiation formulae of F-2(1)tau,beta (a, b;c;z), alongwith relation of F-2(1)tau,beta (a, b;c;z) with the generalized Mittag-Leffler function E-alpha,beta(gamma,q)(z) [Shukla AK, Prajapati JC. On a generalization of Mittag-Leffler function and its properties. J Math Anal Appl. 2007;336(2): 797-811.]. Further properties of the generalized hypergeometric function R-2(1)(a, b;c;t;z) [Virchenko N, Kalla SL, Al-Zamel A. Some results on a generalized hypergeometric function. Integral Transforms Spec Funct. 2001;12(1): 89-100.], namely integral representation and differentiation formulae are also studied.
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