共查询到20条相似文献,搜索用时 39 毫秒
1.
J. D. Zund 《Annali di Matematica Pura ed Applicata》1966,72(1):319-324
Summary An integral formula for the Pontrjagin numbers of a compact orientable real 4k dimensional differentiable manifold which has
a pseudo-Riemannian metric is derived. This formula allows the Pontrjagin numbers to be expressed in terms of the index, or
signature, of the differentiable manifold. The application of these formulae to the four dimensional Lorentzian manifolds
of the general theory of relativity is discussed. A corresponding formula for the Chern numbers of a complex differentiable
manifold with a Hermitian metric is also given. 相似文献
2.
Youn-Seo Choi 《Transactions of the American Mathematical Society》2002,354(2):705-733
Ramanujan's lost notebook contains many results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions. Previously the author proved the first six of Ramanujan's tenth order mock theta function identities. It is the purpose of this paper to prove the seventh and eighth identities of Ramanujan's tenth order mock theta function identities which are expressed by mock theta functions and a definite integral. L. J. Mordell's transformation formula for the definite integral plays a key role in the proofs of these identities. Also, the properties of modular forms are used for the proofs of theta function identities.
3.
《数学物理学报(B辑英文版)》2015,(6)
In the present paper,the authors introduce a new integral transform which yields a number of potentially useful(known or new) integral transfoms as its special cases.Many fundamental results about this new integral transform,which are established in this paper,include(for example) existence theorem,Parseval-type relationship and inversion formula.The relationship between the new integral transform with the H-function and the H-transform are characterized by means of some integral identities.The introduced transform is also used to find solution to a certain differential equation.Some illustrative examples are also given. 相似文献
4.
By evaluating a contour integral with the Cauchy residue theorem, we prove a general summation formula on trigonometric sum, which contains several interesting trigonometric identities as special cases. 相似文献
5.
给出了利用球坐标求解第一型曲面积分的方法及在球坐标系下第一型曲面积分转化为二重积分的公式,实例表明这种方法是可行的.此研究丰富了第一型曲面积分的计算方法,也可为在高校《高等数学》课程教学中对学生能力的培养提供素材. 相似文献
6.
Nelson Faustino 《Mathematical Methods in the Applied Sciences》2019,42(4):1312-1320
In this paper, we exploit the umbral calculus framework to reformulate the so‐called discrete Cauchy‐Kovalevskaya extension in the scope of hypercomplex variables. The key idea is to consider not only formal power series representation for the underlying solution, but also integral representations for the Chebyshev polynomials of first and second kind by means of its Cauchy principal values. It turns out that the resulting integral representation associated to our toy problem is a space‐time Fourier type inversion formula. Moreover, with the aid of some Laplace transform identities involving the generalized Mittag‐Leffler function, we are able to establish a link with a Cauchy problem of differential‐difference type. 相似文献
7.
Using a general q-summation formula, we derive a generating function for the q-Hahn polynomials, which is used to give a complete proof of the orthogonality relation for the continuous q-Hahn polynomials. A new proof of the orthogonality relation for the big q-Jacobi polynomials is also given. A simple evaluation of the Nassrallah–Rahman integral is derived by using this summation formula. A new q-beta integral formula is established, which includes the Nassrallah–Rahman integral as a special case. The q-summation formula also allows us to recover several strange q-series identities. 相似文献
8.
Eric M. Rains 《Transformation Groups》2005,10(1):63-132
We consider two important families of BCn-symmetric polynomials, namely Okounkov's
interpolation polynomials and Koornwinder's orthogonal
polynomials. We give a family of difference equations
satisfied by the former as well as generalizations of the
branching rule and Pieri identity, leading to a number of
multivariate q-analogues of classical hypergeometric
transformations. For the latter, we give new proofs of
Macdonald's conjectures, as well as new identities,
including an inverse binomial formula and several branching
rule and connection coefficient identities. We also derive
families of ordinary symmetric functions that reduce to the
interpolation and Koornwinder polynomials upon appropriate
specialization. As an application, we consider a number
of new integral conjectures associated to classical
symmetric spaces. 相似文献
9.
Anand Dessai 《Mathematische Annalen》1999,315(4):511-528
We study -manifolds with Pin(2)-action. The main tool is a vanishing theorem for certain indices of twisted -Dirac operators. This theorem is used to show that the Witten genus vanishes on such manifolds provided the first Chern class
and the first Pontrjagin class are torsion. We apply the vanishing theorem to cohomology complex projective spaces and give
partial evidence for a conjecture of Petrie. For example we prove that the total Pontrjagin class of a cohomology with -action has standard form if the first Pontrjagin class has standard form. We also determine the intersection form of certain
4-manifolds with Pin(2)-action.
Received: 26 June 1998 相似文献
10.
In this article, two fundamental integral identities including the second-order derivatives of a given function via Riemann–Liouville fractional integrals are established. With the help of these two fractional-type integral identities, all kinds of Hermite–Hadamard-type inequalities involving left-sided and right-sided Riemann–Liouville fractional integrals for m-convex and (s,?m)-convex functions, respectively. Our methods considered here may be a stimulant for further investigations concerning Hermite–Hadamard-type inequalities involving Hadamard fractional integrals. 相似文献
11.
Luis P. Castro Rita C. Guerra Nguyen Minh Tuan 《Mathematical Methods in the Applied Sciences》2020,43(7):4835-4846
We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained. 相似文献
12.
利用旋转曲面方程,以及曲面积分和曲线积分的计算方法,可将旋转曲面的面积通过第一型曲线积分表示出来并进行计算. 相似文献
13.
We establish orthogonality relations for the Baker–Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik–Macdonald–Mehta integral for these functions. As a corollary, we give a simple derivation of the norm identity and Cherednik–Macdonald–Mehta integral for Macdonald polynomials. In the appendix written by the first author, we prove a summation formula for BA functions. We also consider more general identities of Cherednik type, which we use to introduce and construct more general, twisted BA functions. This leads to a construction of new quantum integrable models of Macdonald–Ruijsenaars type. 相似文献
14.
John T. Conway 《Integral Transforms and Special Functions》2016,27(5):371-384
A substantial number of indefinite integrals are presented for the incomplete elliptic integrals of the first and second kinds. The number of new results presented is about three times the total number to be found in the current literature. These integrals were obtained with a Lagrangian method based on the differential equations which these functions obey. All results have been checked numerically with Mathematica. Similar results for the incomplete elliptic integral of the third kind will be presented separately. 相似文献
15.
Zur Izhakian 《Semigroup Forum》2014,88(1):145-161
We show that the submonoid of all n×n triangular tropical matrices satisfies a nontrivial semigroup identity and provide a generic construction for classes of such identities. The utilization of the Fibonacci number formula gives us an upper bound on the length of these 2-variable semigroup identities. 相似文献
16.
Peter Paule 《Journal of Mathematical Analysis and Applications》1985,107(1):255-284
An elementary approach to a number of identities of the Rogers-Ramanujan type is given. It is shown that analytic formulas like, e.g., the Rogers-Ramanujan, the Rogers-Selberg and the Göllnitz-Gordon identities can be obtained essentially as consequences of the q-binomial theorem and the q-Vandermonde formula. 相似文献
17.
<正> 假設一個有限複合形K上的定向S~2叢在K~3上有截面,那末Hopf從他的第二阻礙公式獲得了一個叢不變量△~4()∈H~4(K).Hopf曾經猜測過這個叢不變量與叢的4維示性類有關.本文的目的在證明這個推測是對的,更明確言之,應有 相似文献
18.
基于等距节点积分公式的牛顿迭代法及其收敛阶 总被引:1,自引:0,他引:1
利用等距节点的数值积分公式构造牛顿迭代法的变形格式.我们证明了利用4等分5个节点的Newton-Cotes公式构造的变形牛顿迭代法收敛阶为3,并进一步证明了对于最常用的3等分4节点、5等分6节点、6等分7节点、7等分8节点积分公式,所得到的变形牛顿迭代法收敛阶都是3.最后,本文猜想,利用任意等分的积分公式构造变形牛顿迭代法,所得的迭代格式收敛阶都是3. 相似文献
19.
In a recent note, Santana and Diaz-Barrero proved a number of sum identities involving the well-known Pell numbers. Their
proofs relied heavily on the Binet formula for the Pell numbers. Our goal in this note is to reconsider these identities from
a purely combinatorial viewpoint. We provide bijective proofs for each of the results by interpreting the Pell numbers as
enumerators of certain types of tilings. In turn, our proofs provide helpful insight for straightforward generalizations of
a number of the identities.
Received July 20, 2006 相似文献
20.
Wenchang Chu 《Archiv der Mathematik》2006,87(5):400-406
By applying the derivative operator to Dixon’s formula, we prove several harmonic number identities including one of the hardest
challenge identities conjectured by Weideman (2003).
Received: 28 October 2005 相似文献