scholarly journals The algebra of recurrence relations for exceptional Laguerre and Jacobi polynomials

2020 ◽  
Vol 149 (1) ◽  
pp. 173-188
Author(s):  
Antonio J. Durán
Keyword(s):  
Recurrence Relations ◽  
Jacobi Polynomials

scholarly journals SOME RECURRENCE RELATIONS FOR THE JACOBI POLYNOMIALS P(α,β)n(x)

2015 ◽  
Vol 31 (1) ◽  
pp. 103-107
Author(s):  
Junesang Choi ◽  
Raj S.N. Shine ◽  
Arjun K. Rathie
Keyword(s):  
Recurrence Relations ◽  
Jacobi Polynomials

scholarly journals Calculation of Augmented Jacobi Polynomials by Means of a Recurrence Relation

1980 ◽  
Vol 4 (2) ◽  
pp. 93-97 ◽  
Author(s):  
Zhi-de Liang ◽  
Jia-Zheng Xu ◽  
Fu Wang
Keyword(s):  
Recurrence Relation ◽  
Recurrence Relations ◽  
Jacobi Polynomials

A recurrence relation for Zℓmn(ξ) is deduced from the recurrence relations for Jacobi polynomials. Based on this relation an ALGOL-60 program has been written for efficiently calculating the Zℓmn(ξ) required in ODF analysis.

scholarly journals Multiple big q-Jacobi polynomials

2020 ◽  
Vol 10 (02) ◽  
pp. 2050013
Author(s):  
Fethi Bouzeffour ◽  
Mubariz Garayev
Keyword(s):  
Difference Equation ◽  
Hypergeometric Series ◽  
Recurrence Relations ◽  
Jacobi Polynomials ◽  
Basic Hypergeometric Series ◽  
Type Ii ◽  
Third Order ◽  
Raising And Lowering Operators ◽  
Explicit Formulae ◽  
Lowering Operators

Here, we investigate type II multiple big [Formula: see text]-Jacobi orthogonal polynomials. We provide their explicit formulae in terms of basic hypergeometric series, raising and lowering operators, Rodrigues formulae, third-order [Formula: see text]-difference equation, and we obtain recurrence relations.

Existence of a pair of new recurrence relations for the Meixner-Pollaczek polynomials

2018 ◽  
Vol 11 (3) ◽  
pp. 29-39
Author(s):  
E. I. Jafarov ◽  
A. M. Jafarova ◽  
S. M. Nagiyev
Keyword(s):  
Recurrence Relations ◽  
Pollaczek Polynomials

COMMUNICATION OF COMMON AND MARGINAL CHARACTERISTICS OF CONDITIONS IN A TWO-CHANNEL SYSTEM WITH SIMPLE STREAMLINES OF APPLICATIONS

2017 ◽  
pp. 7-19 ◽  
Author(s):  
Georgiy Aleksandrovich Popov
Keyword(s):  
Operating Systems ◽  
Queue Length ◽  
Recurrence Relations ◽  
Queuing Systems ◽  
Channel System ◽  
Current Period ◽  
Multichannel Systems ◽  
Incoming Call ◽  
Marginal Values ◽  
Time Required

The article deals with a two-channel queuing system with a Poisson incoming call flow, in which the application processing time on each of the devices is different. Such models are used, in particular, when describing the operation of the system for selecting service requests in a number of operating systems. A complex system characteristic was introduced at the time of service endings on at least one of the devices, including the queue length, the remaining service time on the occupied device, and the time since the beginning of the current period of employment. This characteristic determines the state of the system at any time. Recurrence relations are obtained that connect this characteristic with its marginal values when there is no queue in the system. The method of introducing additional events was chosen as one of the main methods for analyzing the model. The relationships presented in this article can be used for analysis of the average characteristics of this system, as well as in the process of its simulation. Summarizing the results of work on multichannel systems with an arbitrary number of servicing devices will significantly reduce the time required for simulating complex systems described by sets of multichannel queuing systems.

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

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