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81.
Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind
Qiu-Ming Luo 《Applied mathematics and computation》2011,217(12):5702-5728
Recently, the authors introduced some generalizations of the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials (see [Q.-M. Luo, H.M. Srivastava, J. Math. Anal. Appl. 308 (2005) 290-302] and [Q.-M. Luo, Taiwanese J. Math. 10 (2006) 917-925]). The main object of this paper is to investigate an analogous generalization of the Genocchi polynomials of higher order, that is, the so-called Apostol-Genocchi polynomials of higher order. For these generalized Apostol-Genocchi polynomials, we establish several elementary properties, provide some explicit relationships with the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials, and derive various explicit series representations in terms of the Gaussian hypergeometric function and the Hurwitz (or generalized) zeta function. We also deduce their special cases and applications which are shown here to lead to the corresponding results for the Genocchi and Euler polynomials of higher order. By introducing an analogue of the Stirling numbers of the second kind, that is, the so-called λ-Stirling numbers of the second kind, we derive some basic properties and formulas and consider some interesting applications to the family of the Apostol type polynomials. Furthermore, we also correct an error in a previous paper [Q.-M. Luo, H.M. Srivastava, Comput. Math. Appl. 51 (2006) 631-642] and pose two open problems on the subject of our investigation. 相似文献
82.
Consider a radioactive decay chain X1 → ? → Xn→ and let Nn(t) be the amount of Xn at time t. This paper establishes error bounds for large-time approximations to Nn(t) that include and generalize the transient equilibrium approximations and other known approximations. The error bounds allow one to find the range of t for which these approximations can be used with a given degree of precision. 相似文献
83.
本文主要研究了一类连续半鞅的极大不等式.利用伊藤公式和Lenglart控制定理,得到了它们的极大不等式,推广了文献[9]的主要结果. 相似文献
84.
The consecutive k-out-of-r-from-n: F system was generalized to multi-state case. This system consists of n linearly ordered components which are at state below j if and only if at least kj components out of any r consecutive are in state below j. In this paper we suggest bounds of increasing multi-state consecutive-k-out-of-r-from-n: F system (k1 ? k2 ? ? ? kM) by applying second order Boole–Bonferroni bounds and applying Hunter–Worsley upper bound. Also numerical results are given. The programs in V.B.6 of the algorithms are available upon request from the authors. 相似文献
85.
利用分析中的解析函数方法和代数中的矩阵方法,得到了m阶常系数齐次线性递推数列通项公式的解析表达式,是对已有结果的完善和推广. 相似文献
86.
87.
针对授课班级出错率较高的一道曲面积分题目,给出四种解法.分析出错的原因在于练习不够外,主要是对重积分概念理解不够透彻. 相似文献
88.
Under the non-Lipschitzian condition, a small time large deviation principle of diffusion processes on Hilbert spaces is established. The operator theory and Gronwall inequality play an important role. 相似文献
89.
The Lanczos method with shift‐invert technique is exploited to approximate the symmetric positive semidefinite Toeplitz matrix exponential. The complexity is lowered by the Gohberg–Semencul formula and the fast Fourier transform. Application to the numerical solution of an integral equation is studied. Numerical experiments are carried out to demonstrate the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献