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Relation between Power Series and Continued Fractions

RELATION BETWEEN POWER SERIES AND CONTINUED FRACTIONS [Pg.91]

Consider an arbitrary formal power series of the form [Pg.91]

It is convenient to define the Hankel determinants formed with the sequence of complex numbers Mo Mi M2 [Pg.91]

The elements of are obtained from the elements of D by advancing the subscripts by unity. In the following we will need also the modified Hankel determinants of the type [Pg.92]

IV. RELATION BETWEEN POWER SERIES AND CONTINUED FRACTIONS... [Pg.91]

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Continued fractions

Continuous fractionation

Continuous power

Fractionating power

Power continued)

Power relational

Power relations

Relation between

Series fractionation