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The equation for a product of solutions of two second-order linear ODEs. / Slavyanov, S. Yu.

2000. 168-171 Paper presented at International Seminar Day on Diffraction Millennium Workshop, DD 2000, Saint Petersburg, Russian Federation.

Research output: Contribution to conferencePaperpeer-review

Harvard

Slavyanov, SY 2000, 'The equation for a product of solutions of two second-order linear ODEs', Paper presented at International Seminar Day on Diffraction Millennium Workshop, DD 2000, Saint Petersburg, Russian Federation, 29/05/00 - 1/06/00 pp. 168-171. https://doi.org/10.1109/DD.2000.902370

APA

Slavyanov, S. Y. (2000). The equation for a product of solutions of two second-order linear ODEs. 168-171. Paper presented at International Seminar Day on Diffraction Millennium Workshop, DD 2000, Saint Petersburg, Russian Federation. https://doi.org/10.1109/DD.2000.902370

Vancouver

Slavyanov SY. The equation for a product of solutions of two second-order linear ODEs. 2000. Paper presented at International Seminar Day on Diffraction Millennium Workshop, DD 2000, Saint Petersburg, Russian Federation. https://doi.org/10.1109/DD.2000.902370

Author

Slavyanov, S. Yu. / The equation for a product of solutions of two second-order linear ODEs. Paper presented at International Seminar Day on Diffraction Millennium Workshop, DD 2000, Saint Petersburg, Russian Federation.4 p.

BibTeX

@conference{41833c7cbe8941fa81556104e80c2765,
title = "The equation for a product of solutions of two second-order linear ODEs",
abstract = "The following problem is studied. Consider two linear homogeneous second-order ordinary differential equations of the form ry″+r′y′=fy (eqn.1) and ru″+r′u′=gu (eqn.2). These equations are chosen to be formally self-adjoint. The function υ(z) is defined as a product of the arbitrary solutions y(z) and g(z) of these equations. υ:=yu. It is assumed that the functions r(z), f(z), and g(z) are analytical functions. Moreover, if applications to special functions are studied then r(z) may be taken a polynomial, and f(z) g(z) are fractions of two polynomials. The question arises: what is the differential equation for which the function υ(z) is a solution? A more sophisticated question is: is there a differential equation for which singularities are located only at the points where singularities of eqs. 1 and 2 are? These are discussed.",
keywords = "Differential equations, Integral equations, Polynomials",
author = "Slavyanov, {S. Yu}",
year = "2000",
month = jan,
day = "1",
doi = "10.1109/DD.2000.902370",
language = "English",
pages = "168--171",
note = "International Seminar Day on Diffraction Millennium Workshop, DD 2000 ; Conference date: 29-05-2000 Through 01-06-2000",

}

RIS

TY - CONF

T1 - The equation for a product of solutions of two second-order linear ODEs

AU - Slavyanov, S. Yu

PY - 2000/1/1

Y1 - 2000/1/1

N2 - The following problem is studied. Consider two linear homogeneous second-order ordinary differential equations of the form ry″+r′y′=fy (eqn.1) and ru″+r′u′=gu (eqn.2). These equations are chosen to be formally self-adjoint. The function υ(z) is defined as a product of the arbitrary solutions y(z) and g(z) of these equations. υ:=yu. It is assumed that the functions r(z), f(z), and g(z) are analytical functions. Moreover, if applications to special functions are studied then r(z) may be taken a polynomial, and f(z) g(z) are fractions of two polynomials. The question arises: what is the differential equation for which the function υ(z) is a solution? A more sophisticated question is: is there a differential equation for which singularities are located only at the points where singularities of eqs. 1 and 2 are? These are discussed.

AB - The following problem is studied. Consider two linear homogeneous second-order ordinary differential equations of the form ry″+r′y′=fy (eqn.1) and ru″+r′u′=gu (eqn.2). These equations are chosen to be formally self-adjoint. The function υ(z) is defined as a product of the arbitrary solutions y(z) and g(z) of these equations. υ:=yu. It is assumed that the functions r(z), f(z), and g(z) are analytical functions. Moreover, if applications to special functions are studied then r(z) may be taken a polynomial, and f(z) g(z) are fractions of two polynomials. The question arises: what is the differential equation for which the function υ(z) is a solution? A more sophisticated question is: is there a differential equation for which singularities are located only at the points where singularities of eqs. 1 and 2 are? These are discussed.

KW - Differential equations

KW - Integral equations

KW - Polynomials

UR - http://www.scopus.com/inward/record.url?scp=84983148823&partnerID=8YFLogxK

U2 - 10.1109/DD.2000.902370

DO - 10.1109/DD.2000.902370

M3 - Paper

AN - SCOPUS:84983148823

SP - 168

EP - 171

T2 - International Seminar Day on Diffraction Millennium Workshop, DD 2000

Y2 - 29 May 2000 through 1 June 2000

ER -

ID: 41278901