共查询到20条相似文献,搜索用时 93 毫秒
1.
利用修正的Abel分部求和引理,系统研究基本超几何级数的部分和,建立一些关于列平衡、二次、三次以及四次基本超几何级数的变换公式和求和公式. 相似文献
2.
本文通过组合反演技巧和级数重组的方法,得到了两个基本超几何级数的变换公式,其中一个的特殊情况包含了著名的Rogers-amanujan恒等式. 相似文献
3.
陈伟 《数学的实践与认识》2004,34(6):155-158
将 C.Krattenthaler的矩阵反演恰当地用于初文昌的恒等式得到了 F.H.Jackson的超几何级数公式 87的推广 . 相似文献
4.
本文主要揭示了Gessel Ira.等给出的拉格朗日反演的q—模拟形式与An-drews G.E.的Bailey引理之间的相互转化的联系,做为例证,给出了利用这些关系得到的古典超几何级数(hypergeometric series)变换和求和公式的新证明,同时得到了模5、7、9、27四个新的Roger’s-Ramanujan类型的恒等式,其具有十分重要的组合意义。 相似文献
5.
张春苟 《数学物理学报(A辑)》2005,(2)
该文讨论了单纯形上Meyer- Konig and Zeller算子的矩量问题.首先得到了二阶矩量在广义积分下的显式表示,并由此导出了二阶矩量的二元Appell超几何函数表示,超几何级数表示和完全渐近公式. 相似文献
6.
应用Carlitz反演的U(n+1)形式以及级数重排技巧,建立了几个基本超几何级数变换公式的U(n+1)拓广. 相似文献
7.
张春苟 《数学物理学报(A辑)》2005,25(2):256-263
该文讨论了单纯形上Meyer Konig and Zeller算子的矩量问题. 首先得到了二阶矩量在广义积分下的显式表示,并由此导出了二阶矩量的二元Appell超几何函数表示,超几何级数表示和完全渐近公式. 相似文献
8.
利用一个基本超几何函数的变换公式及其最基本的求和公式,对Gessel I.和Stanton D。发现的两个Rogers-Ramanujan恒等式,给出一种新的、更为简单的证明。 相似文献
9.
《数学物理学报(A辑)》2016,(1)
该文利用两个二次变换公式建立了两个一般的双重超几何级数变换公式,由此推导出若干新的类型为F_(1:0;μ)~(1:1;λ)和F_(2:0;μ)~(2:1;λ)的双变量超几何级数的简化公式. 相似文献
10.
11.
q-Analogues of two cubic summation formulas that have recently caught the attention of Bill Gosper are found by first showing their connection with the q-binomial formula and then using some known transformation formulas. We also find a q-extension of a cubic transformation formula involving Gauss' hypergeometric function, which turns out to be a relation between balanced and very-well-poised 109 series. 相似文献
12.
A. V. Niukkanen 《Mathematical Notes》2000,67(4):487-494
It is shown that the formulas of operator factorization of hypergeometric functions obtained in the author’s previous works
can be extended to hypergeometric series of the most general form. This generalization does not make the technical apparatus
of the factorization method more complicated. As an example illustrating the practical effectiveness of the formulas obtained
in the paper, we analyze transformation properties of the Horn seriesG
3, whose structure is typical for general hypergeometric functions. It is shown that Erdélyi’s transformation formula relating
the seriesG
3 to the Appell functionF
2, contains erroneous expressions in the arguments ofG
3. The correct analog of Erdélyi’s formula is found, and some new transformations of the seriesG
3 are presented.
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 573–581, April, 2000. 相似文献
13.
Maged G. Bin-Saad 《Journal of Mathematical Analysis and Applications》2011,376(2):451-468
Based upon the classical derivative and integral operators we introduce a new operator which allows the derivation of new symbolic operational images for hypergeometric functions. By means of these symbolic operational images a number of decomposition formulas involving quadruple series are then found. Other closely-related results are also considered. 相似文献
14.
Takumi Noda 《The Ramanujan Journal》2016,41(1-3):183-190
A zeta-function associated with Kummer’s confluent hypergeometric function is introduced as a classical Dirichlet series. An integral representation, a transformation formula, and relation formulas between contiguous functions and one generalization of Ramanujan’s formula are given. The inverse Laplace transform of confluent hypergeometric functions is essentially used to derive the integral representation. 相似文献
15.
Rekha Srivastava 《Applied mathematics and computation》2011,218(3):1077-1083
The main object of this presentation is to show how some simple combinatorial identities can lead to several general families of combinatorial and other series identities as well as summation formulas associated with the Fox-Wright function pΨq and various related generalized hypergeometric functions. At least one of the hypergeometric summation formulas, which is derived here in this manner, has already found a remarkable application in producing several interesting generalizations of the Karlsson-Minton summation formula. We also consider a number of other combinatorial series identities and rational sums which were proven, in recent works, by using different methods and techniques. We show that much more general results can be derived by means of certain summation theorems for hypergeometric series. Relevant connections of the results presented here with those in the aforementioned investigations are also considered. 相似文献
16.
Using series iteration techniques identities and apply each of these identities in we derive a number of general double series order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon. 相似文献
17.
Using series iteration techniques, we derive a number of general double series identities and apply each of these identities in order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon. 相似文献
18.
Rekha Srivastava 《Applied mathematics and computation》2009,215(1):118-124
The main object of the present paper is to investigate some classes of series identities and their applications and consequences leading naturally to several (known or new) hypergeometric reduction formulas. We also indicate how some of these series identities and reduction formulas would yield several series identities which emerged recently in the context of fractional calculus (that is, calculus of integrals and derivatives of any arbitrary real or complex order). 相似文献
19.
《复变函数与椭圆型方程》2012,57(11):807-820
An averaging operator over the roots of unity is defined on a class of analytic functions and its algebraic and analytic properties are investigated. A Cauchy like integral formula for this is obtained. This operator and its properties are then employed to solve higher order Cauchy problems, to derive addition formulas for hypergeometric functions and to obtain integral representations for special classes of hypergeometric functions. 相似文献
20.
We derive summation formulas for a specific kind of multidimensional basic hypergeometric series associated to root systems of classical type. We proceed by combining the classical (one-dimensional) summation formulas with certain determinant evaluations. Our theorems include Ar extensions of Ramanujan's bilateral 1ψ1 sum, Cr extensions of Bailey's very-well-poised 6ψ6 summation, and a Cr extension of Jackson's very-well-poised 8φ7 summation formula. We also derive multidimensional extensions, associated to the classical root systems of type Ar, Br, Cr, and Dr, respectively, of Chu's bilateral transformation formula for basic hypergeometric series of Gasper–Karlsson–Minton type. Limiting cases of our various series identities include multidimensional generalizations of many of the most important summation theorems of the classical theory of basic hypergeometric series. 相似文献