On certain integrals of Lipschitz-Hankel type involving products of bessel functions

Authors

G. Eason, B. Noble, I. N. Sneddon

Type: Article

Publication Date: 1955-04-19

Citations: 3810

DOI: https://doi.org/10.1098/rsta.1955.0005

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Abstract

This paper is concerned with the evaluation and tabulation of certain integrals of the type (* 00 I(p, v; A) = J J fa t) ) e~cttxdt. In part I of this paper, a formula is derived for the integrals in terms of an integral of a hypergeometric function. This new integral is evaluated in the particular cases which are of most frequent use in mathematical physics. By means of these results, approximate expansions are obtained for cases in which the ratio b/a is small or in which b~a and is small. In part II, recurrence relations are developed between integrals with integral values of the parameters pt, v and A. Tables are given by means of which 7(0, 0; 1), 7(0, 1; 1), 7(1, 0; 1), 7(1,1; 1), 7(0, 0 ;0), 7(1, 0;'0), 7(0, 1; 0), 7(1, 1; 0), 7(0,1; - 1 ), 7(1,0; - 1 ) and 7(1,1; - 1 ) may be evaluated for 0 < b/a ^ 2, 0 ^ c/a ^ 2.

Topics

Locations

Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences
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2017-06-01

Yancho Todorov , Petia Koprinkova‐Hristova , Margarita Terziyska

This paper deals with a design methodology for a neural network with improved robust qualities in notion to handling uncertain input data space variations. The proposed network topology combines the … This paper deals with a design methodology for a neural network with improved robust qualities in notion to handling uncertain input data space variations. The proposed network topology combines the simplicity of the radial basis functions networks to interpret or classify data pairs and the abilities of the intuitionistic fuzzy logic to deal with the vagueness of the data space. A simplified gradient optimization procedure as a learning approach for the designed hybrid neural network is proposed. To investigate the effects of the generated structure throughout varying network parameters, the modeling of a two benchmark chaotic time series - Mackey-Glass and Rossler under uncertain conditions is investigated. The obtained results prove the flexibility of the approach and its potentials to cope with data variations.

Thermoelasticity Based on Space-Time-Fractional Heat Conduction Equation

2015-01-01

Yuriy Povstenko

Genetic Optimization of Type-2 Fuzzy Integrators in Ensembles of ANFIS Models for Time Series Prediction

2014-01-01

Jesús Soto , Patricia Melín

Statistical Study of Drink Markets: Case Study

2012-01-22

Seyed Habib A. Rahmati , Arash Haji Karimi , Reza Saffari +1 more

An important official knowledge in each country is to have a comprehensive knowledge about markets of each group of products. Drink markets are one the most important markets of each … An important official knowledge in each country is to have a comprehensive knowledge about markets of each group of products. Drink markets are one the most important markets of each country as a sub-group of nourishment markets. This paper is going to study these markets in Iran. To do so, first, two drink products are selected as pilot, including milk and concentrate. Then, for each product, two groups of information are estimated for the last five years, including 1) total consumption (demand) and 2) total production. Finally, the two groups of productions are compared statistically by means of two statistical tests called t test and Mann-Whitney test. The implemented Different related tables and figures are also illustrated to show the method more explicitly.

Fractional Diffusion in a Solid with Mass Absorption

2017-05-02

Yuriy Povstenko , Tamara Kyrylych , Grażyna Rygał

The space-time-fractional diffusion equation with the Caputo time-fractional derivative and Riesz fractional Laplacian is considered in the case of axial symmetry. Mass absorption (mass release) is described by a source … The space-time-fractional diffusion equation with the Caputo time-fractional derivative and Riesz fractional Laplacian is considered in the case of axial symmetry. Mass absorption (mass release) is described by a source term proportional to concentration. The integral transform technique is used. Different particular cases of the solution are studied. The numerical results are illustrated graphically.

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The research of characters of biorthogonal non-tensor three-dimensional wavelet packets

2010-02-01

Ping Luo , Xinxian Tian

Wavelet analysis is a popular subject in science research. The notion of univariate orthogonal wavelet packets is generalized. First, the notion of biorthogonal nonseparable tri-variate wavelet packets is proposed and … Wavelet analysis is a popular subject in science research. The notion of univariate orthogonal wavelet packets is generalized. First, the notion of biorthogonal nonseparable tri-variate wavelet packets is proposed and a procedure for constructing them is presented. Next, the biorthogonality property of trivariate wavelet packets is investigated, and three biorthogonality formulas of wavelet packets are established.

Research of Financial Time-series Statistical Properties

2021-11-24

Ivan Makarov , Maria Kovaleva , Zinkovich Victoria +1 more

This paper describes the results of research of the stock charts of the cost and trading volume of companies. This task has been reduced to the analysis of statistical properties … This paper describes the results of research of the stock charts of the cost and trading volume of companies. This task has been reduced to the analysis of statistical properties of time series.

Predicting The Level Of Anxiety Of Coronavirus Pandemic Among College Students Using Different Classifier Algorithms

2022-08-25

Febina S. N , Mohamed Mubarak T

The Novel Coronavirus ravaged the entire world, and there was no guarantee that it would ever be wiped out. The purpose of this study is to clarify the factors causing … The Novel Coronavirus ravaged the entire world, and there was no guarantee that it would ever be wiped out. The purpose of this study is to clarify the factors causing anxiety. Anxiety may be brought on by a number of associated circumstances, such as covid. to create the model with the best fit for predicting anxiety and to prioritize the variables that affect anxiety. An online poll was used to gather data, and it asked about global issues, Covid-19 stresses, and (GAD-7). Anxiety levels are rated on this scale from none to severe. The impact of anxiety on these people's quality of life is significant. Since the challenges of college life may act as a trigger for these disorders, college students are particularly sensitive to anxiety. This is especially concerning during the Covid-19 pandemic because new information indicates that students of college age are experiencing increased anxiety. It could have an impact on their academic performance Here, we use classifier techniques to implement anxiety prediction. a series of survey questions, from which we collect information to ascertain whether or not a person would practice anxiety. Finally, we demonstrated the cure for individuals who are concerned and provided advice.

Magnetohydrodynamic flow in a rectangular duct

1987-07-01

M. Tezer‐Sezgin

Abstract The magnetohydrodynamic flow of an incompressible, viscous, electrically conducting fluid in a rectangular duct, with an external magnetic field applied transverse to the flow, has been investigated. One of … Abstract The magnetohydrodynamic flow of an incompressible, viscous, electrically conducting fluid in a rectangular duct, with an external magnetic field applied transverse to the flow, has been investigated. One of the duct's boundaries which is perpendicular to the magnetic field is taken partly insulated, partly conducting. An analytical solution has been developed for the velocity field and magnetic field by reducing the problem to the solution of a Fredholm integral equation of the second kind, which has been solved numerically. Solutions have been obtained for Hartmann numbers M up to 100. All the infinite series obtained are transformed to infinite integrals first and then to finite integrals which contain modified Bessel functions of the second kind. In this way, the difficulties associated with the computation of infinite integrals with oscillating integrands and slowly converging infinite series, the convergence of which is further affected for large values of M , have been avoided. It is found that, as M increases, boundary layers are formed near the non‐conducting boundaries and in the interface region, and a stagnant region is developed in front of the conducting boundary for velocity field. The maximm value of magnetic field takes place on the conducting part. These behaviours are shown on some graphs.

Zarządzanie Przedsiębiorstwem. Enterprise Management

2018-01-01

Duc Tran Anh , Christoph André Dreßler , Eckbert Jankowski

Can transfer function and Bode diagram be obtained from Sumudu transform

2020-01-03

Abdon Atangana , Ali Akgül

In the last past year researchers have relied on the ability of Laplace transform to solve partial, ordinary linear equations with great success. Important analysis in signal analysis including the … In the last past year researchers have relied on the ability of Laplace transform to solve partial, ordinary linear equations with great success. Important analysis in signal analysis including the transfer function, Bode diagram, Nyquist plot and Nichols plot are obtained based on the Laplace transform. The output of the analysis depends only on the results obtained from Laplace transform. However, one weakness of Laplace transform is that the Laplace transform of even function is odd while the Laplace transform of an old function is even which is lack of conservation of properties. On the other hand there exist a similar integral transform known as Sumudu transform has the ability to conserve the properties of the function from real space to complex space. The question that arises in the work, is the following: Can we apply the Sumudu transform to construct new transfer functions that will lead to new Bode, Nichols and Nyquist plots? this question is answered in this work.

IMPROVEMENT OF POWER QUALITY USING SERIES ACTIVE POWER FILTER

2014-04-25

Archana Patnaik

This paper deals with the design and implementation of series active power filter for the improvement of power quality.In power system there is a nonlinear load which seems to be … This paper deals with the design and implementation of series active power filter for the improvement of power quality.In power system there is a nonlinear load which seems to be the prime sources of harmonic distortion.A dissimilar type of load creates nonsinusoidal current from the mains, which give rise to harmonic distortion and affect the power quality.Classic filters may not have satisfactory solutions but series active filter give quite better results and is utilized for the mitigation of harmonics and it also reduces the THD level.Results obtained shows that this scheme is able to mitigate the harmonic problem and can improve the quality of power.This is done by simulation using MATLAB software.

Tables of Complete Elliptic Integrals

1941-04-01

Carl Heuman

Partial Differential Equations of Mathematical Physics

1945-04-01

William T. Reid , H. Bateman