Second-order differential equations
As noted in Chapter 1, most of the functions commonly known as “special functions” are solutions of second-order linear differential equations. These equations occur naturally in certain physical and mathematical contexts. In a certain sense there are exactly two (families of) equations in question: the confluent hypergeometric equation (Kummer’s equation)
with indices (a, c), and the hypergeometric equation
with indices (a, b, c), where a, b, c are constants. The various ...