共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
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
3.
E. V. Karachanskaya 《Siberian Advances in Mathematics》2016,26(1):17-29
For the first time we present a complete proof (from the standpoint of stochastic analysis) of the generalized Itô–Venttsel’ formula whose ideas were adduced in [8]. The proposed proof is an approach to construct the generalized Itô–Venttsel’ formula based on the direct application of the generalized Itô formula and the theory of stochastic approximation in contrast to the proof presented in [17] and based on the method of the integral invariants of a stochastic differential equation. 相似文献
4.
E. Kochneff 《Proceedings of the American Mathematical Society》1996,124(5):1539-1547
We calculate an integral formula for the Hermite projection operators. We give some applications of our formula. We also give a short proof of a recent theorem of Thangavelu.
5.
By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function,and find a new proof of the well-known weighted arithmetic-geometric mean inequality. 相似文献
6.
7.
关于级数敛散性的积分判别法的一个新证明及其推广 总被引:1,自引:0,他引:1
给出了现行的数学分析 ,微积分与高等数学的教材中的数值级数敛散性的积分判别法的一个新证明 ,获得了这个判别法的一个推广 ,由此得到一批渐近公式与命题 相似文献
8.
We provide a new proof of Rademacher's celebrated exact formula for the partition function. Along the way we present a simple treatment of an integral which is ubiquitous in the theory of nonanalytic automorphic forms. 相似文献
9.
A new perspective on a Cauchy integral formula for Clifford algebras valued functions on domains with quite smooth boundaries
was discussed in [5]. On the other hand, the Cauchy transform associated to Clifford analysis has been involved recently with
fractional metric dimensions and fractals, see [1, 2, 3].
In this paper we consider the question of possible generalizations of the Cauchy integral formula to domains with fractal
boundary. As an application, we prove a Martinelli-Bochner type formula for several complex variables on such pathological
domains. The proof makes heavy use of the isotonic approach of the monogenic functions theory.
Received: 8 October 2008 相似文献
10.
11.
《Journal de Mathématiques Pures et Appliquées》2002,81(1):1-33
We consider an h-pseudodifferential operator whose symbol has a closed Hamiltonian trajectory. There exists a Fourier integral operator which quantizes in a natural way the Poincaré map. With the help of this monodromy operator, we give a trace formula which leads to a new proof of the trace formula of Duistermaat–Guillemin and Gutzwiller. 相似文献
12.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(2):105-110
We announce, in the case of the group GSp(4), an equality of two local integrals. One is a Kloosterman integral on the Bessel subgroups of GSp(4) and the other is a Kloosterman integral on the Novodvorsky subgroups of GSp(4). We conjecture that Jacquet's relative trace formula for GL(2) in [7], where Jacquet has given another proof of Waldspurger's result [9], generalizes to GSp(4). We believe that this approach will lead us to a proof and also a precise formulation of a conjecture of Böcherer [1]. Support for this conjecture may be found in the important paper of Böcherer and Schulze-Pillot [2]. Our result serves as the fundamental lemma for our conjectural relative trace formula for the main relevant double cosets. 相似文献
13.
We give a new proof of the Jantzen sum formula for integral representations of Chevalley schemes over Spec Z, except for three exceptional cases. This is done by applying the fixed point formula of Lefschetz type in Arakelov geometry
to generalized flag varieties. Our proof involves the computation of the equivariant Ray-Singer torsion for all equivariant
bundles over complex homogeneous spaces. Furthermore, we find several explicit formulae for the global height of any generalized
flag variety.
Oblatum 17-VI-1999 & 10-IX-2001?Published online: 19 November 2001 相似文献
14.
We provide a proof of Connes’ formula for a representative of the Hochschild class of the Chern character for (p,∞)-summable spectral triples. Our proof is valid for all semifinite von Neumann algebras, and all integral p?1. We employ the minimum possible hypotheses on the spectral triples. 相似文献
15.
Tuo-Yeong Lee 《Czechoslovak Mathematical Journal》2009,59(4):1005-1017
Applying a simple integration by parts formula for the Henstock-Kurzweil integral, we obtain a simple proof of the Riesz representation
theorem for the space of Henstock-Kurzweil integrable functions. Consequently, we give sufficient conditions for the existence
and equality of two iterated Henstock-Kurzweil integrals. 相似文献
16.
We prove the existence of a unique solution for a one-dimensional stochastic parabolic partial differential equation with
random and adapted coefficients perturbed by a two-parameter white noise. The proof is based on a maximal inequality for the
Skorohod integral deduced from It?'s formula for this anticipating stochastic integral.
Received: 21 November 1997 / Revised version: 20 July 1998 相似文献
17.
We prove a generalization to the totally real field case of the Waldspurger’s formula relating the Fourier coefficient of
a half integral weight form and the central value of the L-function of an integral weight form. Our proof is based on a new interpretation of Waldspurger’s formula as a combination
of two ingredients – an equality between global distributions, and a dichotomy result for theta correspondence. As applications
we generalize the Kohnen–Zagier formula for holomorphic forms and prove the equivalence of the Ramanujan conjecture for half
integral weight forms and a case of the Lindel?f hypothesis for integral weight forms. We also study the Kohnen space in the
adelic setting.
The first author was partially supported by NSF grant DMS-0070762. The second author was partially supported by NSF grant
DMS-0355285.
Received: July 2005 Accepted: August 2005 相似文献
18.
We show that the only compact spacelike hypersurfaces in the Lorentz–Minkowski space Ln+1 having nonzero constant scalar curvature and spherical boundary are the hyperbolic caps (with negative constant scalar curvature). One key ingredient in our proof will be an integral formula for the n-dimensional volume enclosed by the boundary of a compact spacelike hypersurface, in the case where the boundary is contained in a hyperplane of Ln+1. As a direct application of that integral formula we also derive an interesting result for the volume of spacelike hypersurfaces. 相似文献
19.
一个计算幂和多项式的积分递推公式 总被引:1,自引:1,他引:0
孙哲 《数学的实践与认识》2004,34(12):149-153
历史悠久的幂和问题 ,是迄今仍然颇受关注的一个问题 .以往虽有多种方法 ,但计算阶数较高的幂和公式大都十分繁琐 ,本文方法则消除了这种不足 .本文介绍一个计算幂和多项式的积分递推公式 ,并给出该公式的初等证明和某些应用 . 相似文献
20.
Jean-Louis Clerc Toshiyuki Kobayashi Bent Ørsted Michael Pevzner 《Mathematische Annalen》2011,349(2):395-431
We find a closed formula for the triple integral on spheres in
_boxclose^2n ^2n ^2n{\mathbb{R}^{2n} \times \mathbb{R}^{2n} \times \mathbb{R}^{2n}} whose kernel is given by powers of the standard symplectic form. This gives a new proof to the Bernstein–Reznikov integral
formula in the n = 1 case. Our method also applies for linear and conformal structures. 相似文献