On linear homogeneous differential equation of Chebyshev type

Abstract

Let L[y] = y(n)(z)+gn-1(z)y(n-1)(z)+. . .+g1(z)y(1)(z)+g0(z)y(z) = 0 be a differential equation of nth order with analytic in circle |z| < R coefficients. We will call above equation by equation of Chebyshev type in |z| < R, if fundamental system of its solution is a Chebyshev system in circle |z| < R . In present paper the conditions with the fulfillment of which the equation L[y] = 0 is of Chebyshev type.

Keywords

• differential equations
• divided differences
• Chebyshev system
• analytic function