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1.
We use elementary methods to prove formulas that represent sums of restricted classes of Schur functions as ratios of determinants. This includes recent formulas for sums over bounded partitions with even parts and sums over bounded partitions whose conjugates have only even parts. All of these formulas imply plane partition generating functions. 相似文献
2.
Miomir S. Stanković Mirjana V. Vidanovic Slobodan B. Tričković 《Applicable analysis》2013,92(1-2):53-64
The series (3) and (4), where T(x) denotes trigonometric integrals (2), are represented as series in terms of Riemann zeta and related functions using the sums of the series (5) and (6), whose terms involve one trigonometric function. These series can be brought in closed form in some cases, where closed form means that the series are represented by finite sums of certain integrals. By specifying the function φ(y) appearing in trigonometric integrals (2) we obtain new series for some special types of functions as well as known results. 相似文献
3.
Francis N. Castro Robin Chapman Luis A. Medina L. Brehsner Sepúlveda 《Discrete Mathematics》2018,341(7):1915-1931
Rotation symmetric Boolean functions are invariant under circular translation of indices. These functions have very rich cryptographic properties and have been used in different cryptosystems. Recently, Thomas Cusick proved that exponential sums of rotation symmetric Boolean functions satisfy homogeneous linear recurrences with integer coefficients. In this work, a generalization of this result is proved over any Galois field. That is, exponential sums over Galois fields of some rotation symmetric polynomials satisfy linear recurrences with integer coefficients. In the particular case of , an elementary method is used to obtain explicit recurrences for exponential sums of some of these functions. The concept of trapezoid Boolean function is also introduced and it is showed that the linear recurrences that exponential sums of trapezoid Boolean functions satisfy are the same as the ones satisfied by exponential sums of the corresponding rotations symmetric Boolean functions. Finally, it is proved that exponential sums of trapezoid and symmetric polynomials also satisfy linear recurrences with integer coefficients over any Galois field . Moreover, the Discrete Fourier Transform matrix and some Complex Hadamard matrices appear as examples in some of our explicit formulas of these recurrences. 相似文献
4.
A. S. Fainleib 《Journal of Theoretical Probability》1998,11(3):609-619
The purpose of this paper is to investigate small values of semi-additive functions and its application to find an upper bound of concentration functions for the sums of independent identically distributed random variables. 相似文献
5.
Weighted trigonometric sums over a half-period 总被引:1,自引:0,他引:1
We derive formulas for evaluating weighted sums of trigonometric functions over evenly-spaced angles in the first quadrant. These results generalize those of a previous paper, where we considered trigonometric sums weighted by real, primitive, non-principal Dirichlet characters. 相似文献
6.
Stavros Garoufalidis James E. Pommersheim 《Journal of the American Mathematical Society》2001,14(1):1-23
We study relations among special values of zeta functions, invariants of toric varieties, and generalized Dedekind sums. In particular, we use invariants arising in the Todd class of a toric variety to give a new explicit formula for the values of the zeta function of a real quadratic field at nonpositive integers. We also express these invariants in terms of the generalized Dedekind sums studied previously by several authors. The paper includes conceptual proofs of these relations and explicit computations of the various zeta values and Dedekind sums involved.
7.
Yu. A. Brychkov 《Applied mathematics and computation》2011,218(3):689-692
A method is proposed for evaluation of some definite integrals and infinite sums containing products of Bessel, Struve and other special functions. 相似文献
8.
U. Passy 《Journal of Optimization Theory and Applications》1978,26(1):97-115
An implicit enumeration technique for solving a certain type of nonconvex program is described. The method can be used for solving signomial programs with constraint functions defined by sums of quasiconcave functions and other types of programs with constraint functions called intrinsically concave functions. A signomial-type example is solved by this method. The algorithm is described together with a convergence proof. No computational results are available at present. 相似文献
9.
General power sums of integers that are,and are not,represented in the two-element Frobenius problem
N. Gauthier 《International Journal of Mathematical Education in Science & Technology》2013,44(6):803-814
A general method is presented for evaluating the sums of mth powers of the integers that can, and that cannot, be represented in the two-element Frobenius problem. Generating functions are introduced and used for that purpose. Explicit formulas for the desired sums are obtained and specific examples are discussed. 相似文献
10.
Takashi Aoki Yasuhiro Kombu Yasuo Ohno 《Proceedings of the American Mathematical Society》2008,136(2):387-395
A generating function for specified sums of multiple zeta values is defined and a differential equation that characterizes this function is given. As applications, some relations for multiple zeta values over the field of rational numbers are discussed.
11.
Miomir S. Stanković Mirjana V. Vidanović Slobodan B. Tricković 《Journal of Computational Analysis and Applications》2003,5(3):313-331
In this paper we consider trigonometric series in terms of the Riemann zeta function and related functions of reciprocal powers. The obtained closed form formulas we apply to the evaluation of the Riemann zeta function and related functions of reciprocal powers. One can establish recursive relations for them and relations between any two of those functions. These closed formulas enable us also to find sums of some Schlömilch series. We give an example which shows how the convergence of a trigonometric series can be accelerated by applying Krylov's method and our formula (7). 相似文献
12.
《Indagationes Mathematicae》2017,28(6):1183-1199
We solve an elementary number theory problem on sums of fractional parts. We apply our result to deduce the finiteness of the image of certain monodromy representations. 相似文献
13.
Régis Blache 《Mathematische Nachrichten》2007,280(15):1681-1697
In this paper we present a new method for evaluating exponential sums associated to a restricted power series in one variable modulo pl , a power of a prime. We show that for sufficiently large l, these sums can be expressed in terms of Gauss sums. Moreover, we study the associated L ‐functions; we show that they are rational, then we determine their degrees and the weights as Weil numbers of their reciprocal roots and poles. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
Shinji Fukuhara Noriko Yui 《Transactions of the American Mathematical Society》2004,356(10):4237-4254
We introduce an elliptic analogue of the Apostol sums, which we call elliptic Apostol sums. These sums are defined by means of certain elliptic functions with a complex parameter having positive imaginary part. When , these elliptic Apostol sums represent the well-known Apostol generalized Dedekind sums. Also these elliptic Apostol sums are modular forms in the variable . We obtain a reciprocity law for these sums, which gives rise to new relations between certain modular forms (of one variable).
15.
由完全正常化缔合勒让德函数构成的球谐级数式,在接近两极时,超高阶次(如超过2500阶次)缔合勒让德函数值的递推计算,达到极大的数量级(超过10的数千次方),产生下溢,这导致一般递推方法失效.本文就缔合勒让德函数的4种常用递推算法,分别进行改进以增加数值稳定性并延缓下溢.最后对由改进算法获得的勒让德函数,结合Horner求和技术,给出计算超高阶球谐级数部分和式的方法. 相似文献
16.
Feng-Zhen Zhao 《Discrete Mathematics》2009,309(12):3830-3842
In this paper, we consider a kind of sums involving Cauchy numbers, which have not been studied in the literature. By means of the method of coefficients, we give some properties of the sums. We further derive some recurrence relations and establish a series of identities involving the sums, Stirling numbers, generalized Bernoulli numbers, generalized Euler numbers, Lah numbers, and harmonic numbers. In particular, we generalize some relations between two kinds of Cauchy numbers and some identities for Cauchy numbers and Stirling numbers. 相似文献
17.
We show that, for a certain class of nonlinear functions of Gaussian sequences, the limiting distribution of normalized sums of the nonlinear function values of a sequence is the convolution of a Gaussian distribution with another non-Gaussian distribution. 相似文献
18.
Jürgen Müller 《Numerical Algorithms》2000,24(3):299-308
Based on a continuity property of the Hadamard product of power series we derive results concerning the rate of convergence
of the partial sums of certain polynomial series expansions for Bessel functions. Since these partial sums are easily computable
by recursion and since cancellation problems are considerably reduced compared to the corresponding Taylor sections, the expansions
may be attractive for numerical purposes. A similar method yields results on series expansions for confluent hypergeometric
functions.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
19.
Polynomial representations of Boolean functions by binary terms are considered. The construction of terms involves variables and residual functions. Special cases of such representations are the decomposition of a function with respect to variables, Zhegalkin polynomials, and representations of functions as sums of conjunctions of residual functions. 相似文献
20.
F. S. Sisser 《Journal of Optimization Theory and Applications》1982,38(4):461-482
Many functions of several variables used in nonlinear programming are factorable, i.e., complicated compositions of transformed sums and products of functions of a single variable. The Hessian matrices of twice-differentiable factorable functions can easily be expressed as sums of outer products (dyads) of vectors. A modified Newton's method for minimizing unconstrained factorable functions which exploits this special form of the Hessian is developed. Computational experience with the method is presented.This material is based upon work supported by the National Science Foundation under Grant No. MCS-79-04106.The author would like to thank Professor G. P. McCormick, George Washington University, for several enlightening discussions on factorable programming and for his valuable comments which improved an earlier version of this paper. 相似文献