power series

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21: 23.17 Elementary Properties

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§23.17(ii) Power and Laurent Series

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22: 28.34 Methods of Computation

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Summation of the power series in §§28.6(i) and 28.15(i) when $\left|q\right|$ is small.

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Summation of the power series in §§28.6(ii) and 28.15(ii) when $\left|q\right|$ is small.

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23: 1.9 Calculus of a Complex Variable

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§1.9(v) Infinite Sequences and Series

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§1.9(vi) Power Series

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Operations

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1.9.60 $${(f(z))}^{\nu }=p_0+p_{1}z+p_2{z}^2+\mathrm{\cdots },$$

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Symbols:

$z$: variable, $\nu$: complex and $p_j$: coefficients

Referenced by:

§1.9(vi)

Permalink:

http://dlmf.nist.gov/1.9.E60

Encodings:

pMML, png, TeX

See also:

Annotations for §1.9(vi), §1.9(vi), §1.9 and Ch.1

… ►Lastly, a power series can be differentiated any number of times within its circle of convergence: …

24: 20.6 Power Series

§20.6 Power Series

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25: 4.24 Inverse Trigonometric Functions: Further Properties

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§4.24(i) Power Series

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26: 19.19 Taylor and Related Series

§19.19 Taylor and Related Series

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27: 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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28: 30.3 Eigenvalues

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§30.3(iv) Power-Series Expansion

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29: 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 $\mathrm{g}\left(z\right)$. …

30: 19.5 Maclaurin and Related Expansions

§19.5 Maclaurin and Related Expansions

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