Logarithmic solution from a repeated Frobenius exponent (source code)

= Logarithmic solution from a repeated Frobenius exponent

= Logarithmic Frobenius solution
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When a second-order equation has a repeated indicial root and only one independent Frobenius series, a second solution has the local form
$$
y_2(z)=y_1(z)\log(z-z_0)+\text{a Frobenius series}.
$$