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 -