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11: 7.17 Inverse Error Functions

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§7.17(ii) Power Series

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12: 14.32 Methods of Computation

… ►In particular, for small or moderate values of the parameters $\mu$ and $\nu$ the power-series expansions of the various hypergeometric function representations given in §§14.3(i)–14.3(iii), 14.19(ii), and 14.20(i) can be selected in such a way that convergence is stable, and reasonably rapid, especially when the argument of the functions is real. …

13: 10.65 Power Series

§10.65 Power Series

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§10.65(iii) Cross-Products and Sums of Squares

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§10.65(iv) Compendia

►For further power series summable in terms of Kelvin functions and their derivatives see Hansen (1975).

14: 28.6 Expansions for Small $q$

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§28.6(i) Eigenvalues

… ►Leading terms of the of the power series for $m=7,8,9,\mathrm{\dots }$ are: … ►

Table 28.6.1: Radii of convergence for power-series expansions of eigenvalues of Mathieu’s equation.

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$n$	${\rho }_n^{(1)}$		${\rho }_n^{(2)}$		${\rho }_n^{(3)}$
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§28.6(ii) Functions ${\mathrm{ce}}_n$ and ${\mathrm{se}}_n$

►Leading terms of the power series for the normalized functions are: …

15: 7.6 Series Expansions

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§7.6(i) Power Series

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16: 23.9 Laurent and Other Power Series

§23.9 Laurent and Other Power Series

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17: 33.23 Methods of Computation

… ►The power-series expansions of §§33.6 and 33.19 converge for all finite values of the radii $\rho$ and $r$, respectively, and may be used to compute the regular and irregular solutions. … ►Thus the regular solutions can be computed from the power-series expansions (§§33.6, 33.19) for small values of the radii and then integrated in the direction of increasing values of the radii. … ►Noble (2004) obtains double-precision accuracy for $W_{-\eta ,\mu }\left(2\rho \right)$ for a wide range of parameters using a combination of recurrence techniques, power-series expansions, and numerical quadrature; compare (33.2.7). …

18: 33.19 Power-Series Expansions in $r$

§33.19 Power-Series Expansions in $r$

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19: 33.6 Power-Series Expansions in $\rho$

§33.6 Power-Series Expansions in $\rho$

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20: 3.10 Continued Fractions

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§3.10(ii) Relations to Power Series

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Stieltjes Fractions

… ►We say that it corresponds to the formal power series … ►For several special functions the $S$-fractions are known explicitly, but in any case the coefficients $a_n$ can always be calculated from the power-series coefficients by means of the quotient-difference algorithm; see Table 3.10.1. … ►We say that it is associated with the formal power series $f(z)$ in (3.10.7) if the expansion of its $n$th convergent $C_n$ in ascending powers of $z$, agrees with (3.10.7) up to and including the term in $z^{2n-1}$, $n=1,2,3,\mathrm{\dots }$. …