### First order linear differential equations with involutive delay and hypergeometric functions

#### 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.

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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