Series Solutions Near a Regular Singular Point

1 Series Solutions Near a Regular Singular Point 

Consider the variable coefficient, linear second-order and homogeneous differential equation 

Presented below is an example that illustrates the essential steps needed to successfully solve Equation 3.63 using Equation 3.66. 

Both sets of constants exhibit a pattern that can be generalized to 

Before the general solution can be stated, it is important to determine if the series obtained in Equation 3.74 and Equation 3.75 are convergent. One way is to apply a convergence test[14]. For example, the ratio test 

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