relations to hypergeometric function

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1: 16.7 Relations to Other Functions

§16.7 Relations to Other Functions

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2: 6.11 Relations to Other Functions

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Confluent Hypergeometric Function

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6.11.2 $$E_1\left(z\right)={\mathrm{e}}^{-z}U(1,1,z),$$

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Symbols:

$U(a,b,z)$: Kummer confluent hypergeometric function, $\mathrm{e}$: base of natural logarithm, $E_1\left(z\right)$: exponential integral and $z$: complex variable

Referenced by:

§6.11, 5th item, §6.6

Permalink:

http://dlmf.nist.gov/6.11.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §6.11, §6.11 and Ch.6

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6.11.3 $$\mathrm{g}\left(z\right)+\mathrm{i}\mathrm{f}\left(z\right)=U(1,1,-\mathrm{i}z).$$

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Symbols:

$U(a,b,z)$: Kummer confluent hypergeometric function, $\mathrm{i}$: imaginary unit, $\mathrm{f}\left(z\right)$: auxiliary function for sine and cosine integrals, $\mathrm{g}\left(z\right)$: auxiliary function for sine and cosine integrals and $z$: complex variable

Referenced by:

§6.11, 5th item

Permalink:

http://dlmf.nist.gov/6.11.E3

Encodings:

pMML, png, TeX

See also:

Annotations for §6.11, §6.11 and Ch.6

3: 16.24 Physical Applications

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§16.24(iii) $\mathit{3}j$, $\mathit{6}j$, and $\mathit{9}j$ Symbols

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4: 15.9 Relations to Other Functions

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§15.9(i) Orthogonal Polynomials

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Krawtchouk

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Meixner

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Meixner–Pollaczek

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§15.9(iii) Gegenbauer Function

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5: 16.18 Special Cases

§16.18 Special Cases

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6: 7.11 Relations to Other Functions

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Confluent Hypergeometric Functions

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Generalized Hypergeometric Functions

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7: 31.7 Relations to Other Functions

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§31.7(i) Reductions to the Gauss Hypergeometric Function

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8: 15.17 Mathematical Applications

… ►This topic is treated in §§15.10 and 15.11. …

9: 13.18 Relations to Other Functions

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§13.18(ii) Incomplete Gamma Functions

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§13.18(iii) Modified Bessel Functions

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§13.18(iv) Parabolic Cylinder Functions

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§13.18(v) Orthogonal Polynomials

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Laguerre Polynomials

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10: 10.39 Relations to Other Functions

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Confluent Hypergeometric Functions

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Generalized Hypergeometric Functions and Hypergeometric Function

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