We show how the integral formula of Poisson for holomorphic functions on the right half plane can be used to quickly evaluate certain integrals from the Table of Gradshteyn and Ryzhik. In addition, we prove a version of this formula for principal value integrals and use it in several ...
608. Class I Representations, Special Functions, and Integral Transforms, vol. 2 (1993), pp. 607. Classical and Quantum Groups and Special Functions, vol. 3 (1992), pp. 629. Dordrecht/Boston/London Kluwer Academic Publisher. A.P. Prudnikov, Yu.A. Brychkov, 0.1. Marichev, Integrals and...
3.In this paper, the author makes use of some properties of elliptic integrals to study the well -known special functionsλ(K).本文利用椭圆积分研究平面拟共形理论中重要的特殊函数λ(K)及其一般形式λ(K。 3)special library function特殊库函数 4)special logical function特殊逻辑函数 1.New method for...
Next, in Sect.5we consider the case of larger values of. This means that the area functional as part of the Helfrich energy is given a bigger weight suggesting that minimisers of the area functional in the class of surfaces of revolution might be useful when minimising the Helfrich funtional...
The amplitude makes sense for thep=n+1andp+1=ncases. The algebraic form of the above integrals can be derived in the soft limit,4k_2.p \rightarrow 1. Using this limit and Appendix B of [66] and [67] one arrives at a closed form for the integrals. For simplicity, we just write...
In this article, we establish some truncated second main theorems for holomorphic curves into projective spaces with some special hypersurfaces and give some applications. In addition, the defect relation, the algebraically degenerate conditions and uniqueness theorem for holomorphic curves with some special...
2015-06-05上传 The geometric complexity of special Lagrangian $T^2$-cones 文档格式: .pdf 文档大小: 500.45K 文档页数: 46页 顶/踩数: 0/0 收藏人数: 0 评论次数: 0 文档热度: 文档分类: 待分类 文档标签: ThegeometriccomplexityofspecialLagrangianT2-cones ...
Many of the well known identities involving the gamma function have generalizations to Γ n for n > 1, including the multiplication formula of Gauss. However, there are no known generalizations of identities for pe- riod integrals like (3). Nevertheless, special values of multiple gamma ...
Ryzhik, Table of Integrals, Series, and Products (Elsevier/Academic Press, Amsterdam, 2007) Google Scholar B.L. Granovsky, H.G. Müller, On the optimality of a class of polynomial kernel functions. Stat. Decis. 7 (4), 301–312 (1989) MathSciNet MATH Google Scholar A. Gretton, K....
Thanks to Yamana [53], each local L-function thus defined is indeed the GCD of the local zeta integrals derived by the doubling method. The complete L-functions and converge absolutely for and they have meromorphic continuations to (see Piatetski-Shapiro and Rallis [41] and also Yamana [53...