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在累次积分的一些计算或证明题中,当先积的那个积分的被积函数的原函数不能用初等函数表达时,往往要交换积分次序,方能计算出结果.本文举例介绍,通过引入积分上限函数,再利用分部积分法,可以使一些特殊的累次积分计算大为简化. 相似文献
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为使F积分得到进一步拓广,我们引入了广义半模F积分[1].本文则讨论由广义半模F积分定义的集函数,指出该集函数对F测度的上、下半连续具有遗传性. 相似文献
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本文提到的特殊函数定积分,是指被积函数的原函数不能用初等函数表达,但其积分值存在的函数的定积分。Euler积分就是一例。计算这类积分主要是利用变量代换。例如计算Euler积分解作代换X=2t,则:就某些题目而言,若在变量代换的同时,再借助Euler积分,则计算会更简便。下面仅举凡例。方法同(Euler积分的变换)。例4求证当a’<1时,积分对第一个积分作变换o+0;一t,对第二个积分作变换点一0一t,对第三个积分作变换0-01一t,故利用Euler积分计算一些特殊函数的定积分@李文华$廊坊陆军导弹学院@李颖$廊坊陆军导弹学院… 相似文献
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研究了圆对称函数的Goluzin问题.当f为圆对称函数,λ=k1(k=2,3,…)时,通过构造一个正实部函数,利用积分方法,得到了k次圆对称函数相邻系数模之差的精确估计.另外,还得到了圆对称函数的积分表示. 相似文献
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在计算被积函数含有绝对值的定积分时,一般说来,要设法把被积函数的绝对值去掉,再进行积分.有些积分要根据被积函数和积分区间的不同情况,采用不同方法进行计算. 相似文献
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Sorin-Mihai Grad 《Optimization》2015,64(8):1759-1775
We deliver formulae for the biconjugate functions of some infimal functions that hold provided the fulfilment of weak regularity conditions of both closedness and interiority types. As special cases, we obtain biconjugates of infimal convolutions of finitely many functions, of optimal value functions of both constrained and unconstrained optimization problems as well as of marginal functions associated with multifunctions (that can be, for instance, convex processes) and some given functions. Moreover, we rediscover or extend different results on biconjugate functions from the literature. 相似文献
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A good portion of Gatteschi’s research publications—about 65%—is devoted to asymptotics of special functions and their zeros. Most prominently among the special functions studied figure classical orthogonal polynomials, notably Jacobi polynomials and their special cases, Laguerre polynomials, and Hermite polynomials by implication. Other important classes of special functions dealt with are Bessel functions of the first and second kind, Airy functions, and confluent hypergeometric functions, both in Tricomi’s and Whittaker’s form. This work is reviewed here, and organized along methodological lines. 相似文献
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We consider tomograms and quasidistributions, such as the Wigner functions, the Glauber–Sudarshan P-functions, and the Husimi Q-functions, that violate the standard normalization condition for probability distribution functions. We introduce special conditions for theWigner function to determine the tomogram with the Radon transform and study three different examples of states like the de Broglie plane wave, the Moshinsky shutter problem, and the stationary state of a charged particle in a uniform constant electric field. We show that their tomograms and quasidistribution functions expressed in terms of the Dirac delta function, the Airy function, and Fresnel integrals violate the standard normalization condition and the density matrix of the state therefore cannot always be reconstructed. We propose a method that allows circumventing this problem using a special tomogram in the limit form. 相似文献
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Ahmed Sebbar 《Milan Journal of Mathematics》2016,84(2):317-347
We give different linear and nonlinear differential relations on Jacobi theta functions with more emphasis on the nonlinear differential equation of the third order of Jacobi. We present different points of view with a special attention to the role played by the second order linear differential equations, and their link to the Riccati equation and the Schwarzian equation. We also study an identity for theta functions resulting from the action of certain infinite order differential operators. 相似文献
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Peter J. Bickel Yaacov Ritov Tobias Rydn 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2002,38(6):825
We consider the log-likelihood function of hidden Markov models, its derivatives and expectations of these (such as different information functions). We give explicit expressions for these functions and bound them as the size of the chain increases. We apply our bounds to obtain partial second order asymptotics and some qualitative properties of a special model as well as to extend some results of [19]. 相似文献
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Alexander V. Rozenblyum 《Acta Appl Math》1992,29(3):171-240
This work is devoted to the construction and investigation of two new classes of special functions, related to representations of groups of motions in the spaces of constant curvature as well as the unitary group of large ranks. These are special functions with matrix indices and some types of orthogonal polynomials in several continuous and discrete variables. The functions introduced generalize a number of classical scalar special functions in one variable. 相似文献
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欧拉Gamma函数是一种非常重要的函数,在数学的许多分支以及物理、工程等学科中都有着十分重要的作用.而完全单调性以及对数完全单调性是Gamma函数的重要性质.主要证明了一些包含Gamma函数和Psi函数在内的特殊函数的完全单调性和对数完全单调性,并由此推出了一些重要的不等式. 相似文献
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Dr. U. Derigs 《Mathematical Methods of Operations Research》1979,23(7):251-267
For special combinatorial optimization problems different kind of objective functions are of practical interest. In this paper we investigate the applicability ofBurkard's duality concept for algebraic objective functions. Thereafter we discuss the concept of admissible transformations, a more combinatorial motivated way of problem solving which enables us to treat different objective functions in one approach. We demonstrate the applicability of this approach to special combinatorial optimization problems.
Zusammenfassung Bei der Behandlung spezieller kombinatorischer Optimierungsaufgaben sind verschiedene Zielfunktionen von praktischer Bedeutung. In dieser Arbeit untersuchen wir zunächst die Anwendbarkeit einer Dualitätstheorie für algebraische Zielfunktionen, die vonBurkard vorgeschlagen wurde. Danach diskutieren wir das Konzept der zulässigen Transformationen, einen mehr kombinatorisch motivierten Zugang, der es erlaubt verschiedene relevante Zielfunktionen in einem Ansatz zu behandeln. Wir demonstrieren die Anwendbarkeit dieses Konzeptes bei speziellen kombinatorischen Optimierungsproblemen.相似文献