power-series expansions

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21: 33.20 Expansions for Small $|ϵ|$

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§33.20(ii) Power-Series in $ϵ$ for the Regular Solution

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22: 22.15 Inverse Functions

… ►For power-series expansions see Carlson (2008).

23: 6.18 Methods of Computation

… ►For small or moderate values of $x$ and $|z|$, the expansion in power series (§6.6) or in series of spherical Bessel functions (§6.10(ii)) can be used. … ►Power series, asymptotic expansions, and quadrature can also be used to compute the functions $\mathrm{f}\left(z\right)$ and $\mathrm{g}\left(z\right)$. …

24: 11.9 Lommel Functions

… ►where $A$, $B$ are arbitrary constants, $s_{\mu ,\nu }\left(z\right)$ is the Lommel function defined by …

25: 7.18 Repeated Integrals of the Complementary Error Function

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26: 29.3 Definitions and Basic Properties

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§29.3(vii) Power Series

►For power-series expansions of the eigenvalues see Volkmer (2004b).

27: 8.21 Generalized Sine and Cosine Integrals

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Power-Series Expansions

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28: 12.14 The Function $W(a,x)$

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§12.14(v) Power-Series Expansions

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29: 7.11 Relations to Other Functions

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30: 27.13 Functions

… ►Mordell (1917) notes that $r_k\left(n\right)$ is the coefficient of $x^n$ in the power-series expansion of the $k$th power of the series for $\vartheta \left(x\right)$. …