power function

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21: 11.9 Lommel Functions

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

22: 13.14 Definitions and Basic Properties

… ►The series … ►

13.14.9 $$W_{\kappa ,\pm \frac{1}{2}n}\left(z\right)={(-1)}^{\kappa -\frac{1}{2}n-\frac{1}{2}}{\mathrm{e}}^{-\frac{1}{2}z}{z}^{\frac{1}{2}n+\frac{1}{2}}\sum _{k=0}^{\kappa -\frac{1}{2}n-\frac{1}{2}}\left(\genfrac{}{}{0.0pt}{}{\kappa -\frac{1}{2}n-\frac{1}{2}}{k}\right){\left(n+1+k\right)}_{\kappa -k-\frac{1}{2}n-\frac{1}{2}}{(-z)}^k,$$ $\kappa -\frac{1}{2}n-\frac{1}{2}=0,1,2,\mathrm{\dots }$.

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Symbols:

${\left(a\right)}_n$: Pochhammer’s symbol (or shifted factorial), $W_{\kappa ,\mu }\left(z\right)$: Whittaker confluent hypergeometric function, $\left(\genfrac{}{}{0.0pt}{}{m}{n}\right)$: binomial coefficient, $\mathrm{e}$: base of natural logarithm, $n$: nonnegative integer and $z$: complex variable

Referenced by:

§13.14(i)

Permalink:

http://dlmf.nist.gov/13.14.E9

Encodings:

pMML, png, TeX

See also:

Annotations for §13.14(i), §13.14(i), §13.14 and Ch.13

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23: 30.3 Eigenvalues

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§30.3(iv) Power-Series Expansion

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24: 22.15 Inverse Functions

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25: 11.2 Definitions

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§11.2(i) Power-Series Expansions

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26: 4.38 Inverse Hyperbolic Functions: Further Properties

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§4.38(i) Power Series

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27: 7.18 Repeated Integrals of the Complementary Error Function

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28: 20.11 Generalizations and Analogs

… ►In the case $z=0$ identities for theta functions become identities in the complex variable $q$, with , that involve rational functions, power series, and continued fractions; see Adiga et al. (1985), McKean and Moll (1999, pp. 156–158), and Andrews et al. (1988, §10.7). …

29: 28.6 Expansions for Small $q$

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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: …

30: 12.14 The Function $W(a,x)$

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§12.14(v) Power-Series Expansions

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