Series indicial equation

This equation cannot be solved by expansion in series, as the coefficients of S(p) and its first derivative result in a singularity at p = 0. Because this point is regular, the substitution Sip) = ps (p) is suggested. If the coefficient of p 2 is set equal to zero, the resulting indicial equation is... 

This equation, which determines the powers of the Frobenius series is called the indicial equation and it has solutions m = 0orm = l. The coefficient of the next power must also vanish ... 

The possible values of a are obtained from the indicial equation, which is based on tbe presumption that ao is the first nonzero coefficient in the series (8.121). 

As stated earlier, the first stage is to find the values for c, through an indicial equation. This is obtained by inspecting the coefficients of the lowest powers in the respective series expansions. Consider Eq. 3.29 with P x), Qix) given by Eqs. 3.30 and 3.31 first, perform the differentiations... 

Substituting this series in 4 129 gives the indicial equation... 

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