fractional derivatives

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31: 29.3 Definitions and Basic Properties

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§29.3(iii) Continued Fractions

… ►satisfies the continued-fraction equation … ►The continued fraction following the second negative sign on the left-hand side of (29.3.10) is finite: it equals 0 if $p=0$, and if $p>0$, then the last denominator is ${\beta }_0-H$. If $\nu$ is a nonnegative integer and $2p\le \nu$, then the continued fraction on the right-hand side of (29.3.10) terminates, and (29.3.10) has only the solutions (29.3.9) with $2m\le \nu$. … ►To complete the definitions, ${\mathrm{𝐸𝑐}}_{\nu }^m(K,k^2)$ is positive and ${d{\mathrm{𝐸𝑠}}_{\nu }^m(z,k^2)/dz|}_{z=K}$ is negative. …