scholarly journals A generalized Birkhoff–Young quadrature formula

2016 ◽  
Vol 32 (2) ◽  
pp. 203-213
Author(s):  
GRADIMIR V. MILOVANOVIC ◽  
◽  
MILOLJUB ALBIJANIC ◽  
Keyword(s):  
Numerical Integration ◽  
Explicit Form ◽  
Quadrature Formula ◽  
Analytic Functions ◽  
Maximal Degree ◽  
Special Cases

A generalized (4n + 1)-point Birkhoff–Young quadrature of interpolatory type with the maximal degree of precision for numerical integration of analytic functions is derived. An explicit form of the node polynomial of such kind of quadratures is obtained. Special cases and an example are presented.

Formulation of Equations of Motion for Systems Subject to Constraints

1985 ◽  
Vol 52 (2) ◽  
pp. 465-470 ◽  
Author(s):  
C. Wampler ◽  
K. Buffinton ◽  
J. Shu-hui
Keyword(s):  
Numerical Integration ◽  
Explicit Form ◽  
Equations Of Motion ◽  
Constrained Systems ◽  
Dynamical Equations ◽  
Special Cases ◽  
Additional Constraints

A method for constructing equations of motion governing constrained systems is presented. The method, which is particularly useful when equations of motion have already been formulated, and new equations of motion, reflecting the presence of additional constraints are needed, allow the new equations to be written as a recombination of terms comprising the original equations. An explicit form in which the new dynamical equations may be cast for the purpose of numerical integration is developed, along with special cases that demonstrate how the procedure may be simplified in two commonly occurring situations. An illustrative example from the field of robotics is presented, and several areas of application are identified.

scholarly journals The truncated Hyper-Poisson queues: Hk/Ma,b/C/N with balking, reneging and general bulk service rule

2008 ◽  
Vol 18 (1) ◽  
pp. 23-36 ◽  
Author(s):  
A.I. Shawky ◽  
M.S. El-Paoumy
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Explicit Form ◽  
Recurrence Relations ◽  
Expected Number ◽  
Special Cases ◽  
Queue Discipline ◽  
Bulk Service ◽  
General Bulk Service Rule ◽  
Steady State Probabilities

The aim of this paper is to derive the analytical solution of the queue: Hk/Ma,b/C/N with balking and reneging in which (I) units arrive according to a hyper-Poisson distribution with k independent branches, (II) the queue discipline is FIFO; and (III) the units are served in batches according to a general bulk service rule. The steady-state probabilities, recurrence relations connecting various probabilities introduced are found and the expected number of units in the queue is derived in an explicit form. Also, some special cases are obtained. .

scholarly journals Addition Formula and Related Integral Equations for Heine—Stieltjes Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1231
Author(s):  
Hans Volkmer
Keyword(s):  
Integral Equations ◽  
Explicit Form ◽  
Spherical Harmonics ◽  
Reproducing Kernel ◽  
Addition Formula ◽  
Symmetric Products ◽  
Special Cases ◽  
Related Integral ◽  
Generalized Spherical Harmonics ◽  
The Relationship

It is shown that symmetric products of Heine–Stieltjes quasi-polynomials satisfy an addition formula. The formula follows from the relationship between Heine–Stieltjes quasi-polynomials and spaces of generalized spherical harmonics, and from the known explicit form of the reproducing kernel of these spaces. In special cases, the addition formula is written out explicitly and verified. As an application, integral equations for Heine–Stieltjes quasi-polynomials are found.

General series involving H-functions

1969 ◽  
Vol 65 (2) ◽  
pp. 461-465
Author(s):  
R. N. Jain
Keyword(s):  
Hypergeometric Function ◽  
Analytic Functions ◽  
General Nature ◽  
Complex Numbers ◽  
Important Class ◽  
Vast Number ◽  
Finite Series ◽  
General Series ◽  
Special Cases ◽  
Image Position

MacRobert (4–7) and Ragab(8) have summed many infinite and finite series of E-functions by expressing the E-functions as Barnes integrals and interchanging the order of summation and integration. Verma (9) has given two general expansions involving E-functions from which, in addition to some new results, all the expansions given by MacRobert and Ragab can be deduced. Proceeding similarly, we have studied general summations involving H-functions. The H-function is the most generalized form of the hypergeometric function. It contains a vast number of well-known analytic functions as special cases and also an important class of symmetrical Fourier kernels of a very general nature. The H-function is defined as (2)where 0 ≤ n ≤ p, 1 ≤ m ≤ q, αj, βj are positive numbers and aj, bj may be complex numbers.

scholarly journals Neighborhoods of certain classes of analytic functions with negative coefficients

2006 ◽  
Vol 2006 ◽  
pp. 1-6 ◽  
Author(s):  
M. K. Aouf
Keyword(s):  
Analytic Functions ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Special Cases ◽  
Inclusion Relations

By making use of the familiar concept of neighborhoods of analytic functions, the author proves several inclusion relations associated with the(n,δ)-neighborhoods of various subclasses defined by Salagean operator. Special cases of some of these inclusion relations are shown to yield known results.

scholarly journals Generalization properties for certain analytic functions

1998 ◽  
Vol 21 (4) ◽  
pp. 707-712 ◽  
Author(s):  
Shigeyoshi Owa
Keyword(s):  
Analytic Functions ◽  
Special Cases

The object ofthe present paper is to give some generalizations of results for certain analytic functions which were proved by Saitoh (Math. Japon. 35 (1990), 1073-1076). Our results contain some corollaries as the special cases.

scholarly journals Certain Subclasses of Multivalent Functions Defined by Higher-Order Derivative

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Xiaofei Li ◽  
Deng Ding ◽  
Liping Xu ◽  
Chuan Qin ◽  
Songbo Hu
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Higher Order ◽  
Order Derivative ◽  
Special Cases ◽  
Higher Order Derivative ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In this paper, we define and study some subclasses of multivalent analytic functions of higher order in the unit disc. These classes generalize some classes previously studied. We obtain coefficient inequalities, distortion theorems, extreme points, and integral mean inequalities. We derive some results as special cases.

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