Series solution and special functions
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The solution of ordinary linear differential equations of second order with variable coefficients in the form of an infinite convergent series is called solution in series or integration in series.
The series solution of certain differential equations give rise to special functions such as
Bessel's function, Legendre's polynomials, Laguerre's polynomial, Hermite's polynomial, Chebyshev polynomials. These special functions have wide applications in engineering.
In this unit, we will discuss methods of solution of second order linear differential
equations with variable coefficients in series along with Bessel's function, Legendre's polynomial and their properties.