General Definitions of Integral Transforms for Mathematical Physics

2020 ◽  
Vol 70 (9) ◽  
pp. 759-765
Author(s):  
Dongseung KANG ◽  
Hoewoon KIM ◽  
Bongwoo LEE*
Keyword(s):  
Integral Transforms ◽  
Mathematical Physics

scholarly journals Some Schemata for Applications of the Integral Transforms of Mathematical Physics

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 254 ◽  
Author(s):  
Yuri Luchko
Keyword(s):  
Differential Equations ◽  
Integral Transform ◽  
First Integral ◽  
Integral Transforms ◽  
Mathematical Physics ◽  
Basic Properties ◽  
Survey Article ◽  
Laplace Integral ◽  
Generating Operators

In this survey article, some schemata for applications of the integral transforms of mathematical physics are presented. First, integral transforms of mathematical physics are defined by using the notions of the inverse transforms and generating operators. The convolutions and generating operators of the integral transforms of mathematical physics are closely connected with the integral, differential, and integro-differential equations that can be solved by means of the corresponding integral transforms. Another important technique for applications of the integral transforms is the Mikusinski-type operational calculi that are also discussed in the article. The general schemata for applications of the integral transforms of mathematical physics are illustrated on an example of the Laplace integral transform. Finally, the Mellin integral transform and its basic properties and applications are briefly discussed.

scholarly journals Matrix Fourier Transforms for Consistent Mathematical Models

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Oleg Yaremko ◽  
Natalia Yaremko
Keyword(s):  
Mathematical Models ◽  
Fourier Transforms ◽  
Integral Form ◽  
Integral Transforms ◽  
Mathematical Physics ◽  
Discontinuous Coefficients ◽  
Piecewise Homogeneous Media ◽  
Fourier Matrix ◽  
Matrix Transforms ◽  
Homogeneous Media

We create a matrix integral transforms method; it allows us to describe analytically the consistent mathematical models. An explicit constructions for direct and inverse Fourier matrix transforms with discontinuous coefficients are established. We introduce special types of Fourier matrix transforms: matrix cosine transforms, matrix sine transforms, and matrix transforms with piecewise trigonometric kernels. The integral transforms of such kinds are used for problems solving of mathematical physics in homogeneous and piecewise homogeneous media. Analytical solution of iterated heat conduction equation is obtained. Stress produced in the elastic semi-infinite solid by pressure is obtained in the integral form.

Integral Transforms in Mathematical Physics

1968 ◽  
Vol 52 (382) ◽  
pp. 416
Author(s):  
D. S. Jones ◽  
C. J. Tranter
Keyword(s):  
Integral Transforms ◽  
Mathematical Physics

A family of the incomplete hypergeometric functions and associated integral transform and fractional derivative formulas

Filomat ◽  
2017 ◽  
Vol 31 (1) ◽  
pp. 125-140 ◽  
Author(s):  
Rekha Srivastava ◽  
Ritu Agarwal ◽  
Sonal Jain
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Derivatives ◽  
Integral Transform ◽  
Special Functions ◽  
Applied Mathematics ◽  
Integral Transforms ◽  
Mathematical Physics ◽  
Natural Generalization ◽  
Derivative Formulas ◽  
Derivatives Of

Recently, Srivastava et al. [Integral Transforms Spec. Funct. 23 (2012), 659-683] introduced the incomplete Pochhammer symbols that led to a natural generalization and decomposition of a class of hypergeometric and other related functions as well as to certain potentially useful closed-form representations of definite and improper integrals of various special functions of applied mathematics and mathematical physics. In the present paper, our aim is to establish several formulas involving integral transforms and fractional derivatives of this family of incomplete hypergeometric functions. As corollaries and consequences, many interesting results are shown to follow from our main results.

Integral Transforms in Mathematical Physics.

1957 ◽  
Vol 64 (5) ◽  
pp. 378
Author(s):  
R. B. Deal ◽  
C. J. Tranter
Keyword(s):  
Integral Transforms ◽  
Mathematical Physics

scholarly journals Numerical Values of Some Integrals involving Bessel Functions

1962 ◽  
Vol 13 (1) ◽  
pp. 87-113 ◽  
Author(s):  
D. L. George
Keyword(s):  
Boundary Value Problems ◽  
Bessel Functions ◽  
Boundary Value ◽  
Integral Transforms ◽  
Mathematical Physics ◽  
Image Position

In the solution of boundary value problems in mathematical physics by means of integral transforms, we often find that the solution of a particular problem can be expressed in terms of integrals of the typewhere r and z are positive, and v and n are integers satisfying the convergencecondition v+n>−1.

Integral Transforms in Mathematical Physics

1952 ◽  
Vol 20 (3) ◽  
pp. 186-187 ◽  
Author(s):  
C. J. Tranter ◽  
Alfred Leitner
Keyword(s):  
Integral Transforms ◽  
Mathematical Physics

Integral Transforms in Mathematical Physics

1952 ◽  
Vol 36 (317) ◽  
pp. 215
Author(s):  
P. T. Landsberg ◽  
C. J. Tranter
Keyword(s):  
Integral Transforms ◽  
Mathematical Physics

scholarly journals Evaluation of Certain Integrals Involving Bessel Functions

1963 ◽  
Vol 13 (4) ◽  
pp. 285-290 ◽  
Author(s):  
E. Deutsch
Keyword(s):  
Boundary Value Problems ◽  
Bessel Functions ◽  
Boundary Value ◽  
Integral Transforms ◽  
Mathematical Physics ◽  
Convergence Condition ◽  
Image Position

In the solution of boundary value problems in mathematical physics by means of integral transforms we often find that the solution of a particular problem can be expressed in terms of integrals of the typewhere r and z are positive and m and n are integers satisfying the convergence condition m+n>−2.

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