Expressions of solutions of ordinary differential equations by standard functions

Abstract

It is well known that solutions of many ordinary differential equations allow presentation in the power series form. In the paper we introduce and analyze rigorous conditions under which the later series (solutions) can be reduced to a finite sum of standard functions. Some areas of practical applicability of the proposed algorithm are discussed.

Key words:

• differential equations
• algebraic progression
• Van‐der‐Mond determinant
• standard functions