First order linear differential equations with involutive delay and hypergeometric functions

Stefan Czekalski, Henryk Żołądek

DOI: http://dx.doi.org/10.12775/TMNA.2017.002

Abstract


We present an alternative approach to functions satisfying second order
linear ordinary differential equations. It turns out that many of them
satisfy a first order ordinary differential equation with an involution. The
involution acts on the argument as well as on parameters. Basic examples
involve the hypergeometric functions and their descendants.

Keywords


Differential equation with an involution; hypergeometric equation; Chebyshev equation

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