# §16.21 Differential Equation

satisfies the differential equation

where again . This equation is of order . In consequence of (16.19.1) we may assume, without loss of generality, that . With the classification of §16.8(i), when the only singularities of (16.21.1) are a regular singularity at and an irregular singularity at . When the only singularities of (16.21.1) are regular singularities at , , and .

A fundamental set of solutions of (16.21.1) is given by

For other fundamental sets see Erdélyi et al. (1953a, §5.4) and Marichev (1984).