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1.
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). 相似文献
2.
We prove some convexity properties for a sum of hypergeometric functions and obtain a generalization of Legendre's relation for complete elliptic integrals. We apply these results to prove some inequalities for hypergeometric functions, incomplete beta-functions, and Legendre functions. 相似文献
3.
Multivariate hypergeometric functions associated with toric varieties were introduced by Gel'fand, Kapranov and Zelevinsky. Singularities of such functions are discriminants, that is, divisors projectively dual to torus orbit closures. We show that most of these potential denominators never appear in rational hypergeometric functions. We conjecture that the denominator of any rational hypergeometric function is a product of resultants, that is, a product of special discriminants arising from Cayley configurations. This conjecture is proved for toric hypersurfaces and for toric varieties of dimension at most three. Toric residues are applied to show that every toric resultant appears in the denominator of some rational hypergeometric function. 相似文献
4.
In this paper we give analogues of the Ramanujan functions and nonlinear differential equations for them. Investigating a modular structure of solutions for nonlinear differential systems, we deduce new identities between the Ramanujan and hypergeometric functions. Another result of this paper is a solution of transcendence problems concerning nonlinear systems. 相似文献
5.
In a recent paper, Ono and Penniston proved a family of congruences for 3
F
2 hypergeometric functions over finite fields. They use the relationship between these functions and the arithmetic of a certain family of elliptic curves to obtain their congruences. Here we prove analogous congruences for 2
F
1 hypergeometric functions. 相似文献
6.
We introduce hypergeometric functions related to projective Schur functions Q
and describe their properties. Linear equations, integral representations, and Pfaffian representations are obtained. These hypergeometric functions are vacuum expectations of free fermion fields and are therefore tau functions of the so-called BKP hierarchy of integrable equations. 相似文献
7.
Efficient methods for the computation of the real zeros of hypergeometric functions which are solutions of second order ODEs are described. These methods are based on global fixed point iterations which apply to families of functions satisfying first order linear difference differential equations with continuous coefficients. In order to compute the zeros of arbitrary solutions of the hypergeometric equations, we have at our disposal several different sets of difference differential equations (DDE). We analyze the behavior of these different sets regarding the rate of convergence of the associated fixed point iteration. It is shown how combinations of different sets of DDEs, depending on the range of parameters and the dependent variable, is able to produce efficient methods for the computation of zeros with a fairly uniform convergence rate for each zero. 相似文献
8.
We will provide sufficient conditions for the shifted hypergeometric function \(z_2F_1(a,b;c;z)\) to be a member of a specific subclass of starlike functions in terms of the complex parameters a, b and c. For example, we study starlikeness of order \(\alpha ,\) \(\lambda \)-spirallikeness of order \(\alpha \) and strong starlikeness of order \(\alpha .\) In particular, those properties lead to univalence of the shifted hypergeometric functions on the unit disk. 相似文献
9.
S. Agrawal 《Journal of Difference Equations and Applications》2013,19(11):1502-1522
In this article, we consider basic hypergeometric functions introduced by Heine. We study the mapping properties of certain ratios of basic hypergeometric functions having shifted parameters and show that they map the domains of analyticity onto domains convex in the direction of the imaginary axis. In order to investigate these mapping properties, some useful identities are obtained in terms of basic hypergeometric functions. In addition, we find conditions under which the basic hypergeometric functions are in a q-close-to-convex family. 相似文献
10.
A. Yu. Orlov 《Theoretical and Mathematical Physics》2006,146(2):183-206
It is known that resonant multisoliton solutions depend on higher times and a set of parameters (integrals of motion). We
show that soliton tau functions of the Toda lattice (and of the multicomponent Toda lattice) are tau functions of a dual hierarchy,
where the higher times and the parameters (integrals of motion) exchange roles. The multisoliton solutions turn out to be
rational solutions of the dual hierarchy, and the infinite-soliton tau functions turn out to be hypergeometric-type tau functions
of the dual hierarchy. The variables in the dual hierarchies exchange roles. Soliton momenta are related to the Frobenius
coordinates of partitions in the decomposition of rational solutions with respect to Schur functions. As an example, we consider
partition functions of matrix models: their perturbation series is, on one hand, a hypergeometric tau function and, on the
other hand, can be interpreted as an infinite-soliton solution.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 2, pp. 222–250, February, 2006. 相似文献
11.
α型β级Bazilevic函数的Fekete-Szeg?问题 总被引:14,自引:0,他引:14
设B(α,β)(α>0,0≤β<1)表示在单位圆盘内定义的规范化的α型β级Bazilevic函数类.本文对B(α,β)中函数f(z)=z+∑from∞to(n=2)anzn得到|a3-λa22|(0≤λ≤1)的准确估计. 相似文献
12.
In a paper by K. Driver and P. Duren (1999, Numer. Algorithms21, 147–156) a theorem of Borwein and Chen was used to show that for each k
the zeros of the hypergeometric polynomials F(−n, kn+1; kn+2; z) cluster on the loop of the lemniscate {z: |zk(1−z)|=kk/(k+1)k+1}, with Re{z}>k/(k+1) as n→∞. We now supply a direct proof which generalizes this result to arbitrary k>0, while showing that every point of the curve is a cluster point of zeros. Examples generated by computer graphics suggest some finer asymptotic properties of the zeros. 相似文献
13.
14.
We give the hypergeometric solutions of some algebraic equations including the general fifth-degree equation. 相似文献
15.
Understanding of wave propagation problems is enhanced by consideringgeneralizations to differential equations of order 2n. In particular,reflection and coupling of waves at transition points can involvecertain types of generalized hypergeometric functions. In thispaper, properties of oF2n-1 functions are considered systematically,when the parameters are specially chosen for application totransition points; a wide range of interesting properties unfolds,which recall the properties of Bessel functions when n = 1. 相似文献
16.
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18.
In this paper, we refine work of Beukers, applying results from the theory of Padé approximation to (1 – z)1/2 to the problem of restricted rational approximation to quadratic irrationals. As a result, we derive effective lower bounds for rational approximation to
(where m is a positive nonsquare integer) by rationals of certain types. Forexample, we have
provided q is a power of 2 or 3, respectively. We then use this approach to obtain sharp bounds for the number of solutions to certain families of polynomial-exponential Diophantine equations. In particular, we answer a question of Beukers on the maximal number of solutions of the equation x
2 + D = p
n where D is a nonzero integer and p is an odd rational prime, coprime to D. 相似文献
19.
Two stable sampling formulas for reconstructing analytic functions from exponentially spaced samples are considered. Criterion for selecting regularization parameter and error estimates are obtained. 相似文献