relation to confluent hypergeometric functions

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1: 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

2: 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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3: 13.6 Relations to Other Functions

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§13.6(ii) Incomplete Gamma Functions

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§13.6(iii) Modified Bessel Functions

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§13.6(v) Orthogonal Polynomials

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Laguerre Polynomials

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Charlier Polynomials

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4: 7.11 Relations to Other Functions

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Confluent Hypergeometric Functions

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5: 10.16 Relations to Other Functions

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Confluent Hypergeometric Functions

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6: 8.5 Confluent Hypergeometric Representations

§8.5 Confluent Hypergeometric Representations

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7: 10.39 Relations to Other Functions

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Confluent Hypergeometric Functions

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8: 33.2 Definitions and Basic Properties

… ►The function $F_{\mathrm{\ell }}(\eta ,\rho )$ is recessive (§2.7(iii)) at $\rho =0$, and is defined by … ►The functions $H_{\mathrm{\ell }}^{\pm }(\eta ,\rho )$ are defined by …

9: 8.19 Generalized Exponential Integral

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§8.19(vi) Relation to Confluent Hypergeometric Function

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10: 12.7 Relations to Other Functions

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§12.7(iv) Confluent Hypergeometric Functions

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