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11: 6.11 Relations to Other Functions

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6.11.1 $$E_1\left(z\right)=\mathrm{\Gamma }(0,z).$$

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Symbols:

$E_1\left(z\right)$: exponential integral, $\mathrm{\Gamma }(a,z)$: incomplete gamma function and $z$: complex variable

A&S Ref:

5.1.45 (specialcase of)

Referenced by:

§6.11

Permalink:

http://dlmf.nist.gov/6.11.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §6.11, §6.11 and Ch.6

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12: 16.24 Physical Applications

… ►Lastly, special cases of the $\mathit{9}j$ symbols are ${}_5{}^{}F_4^{}$ functions with unit argument. …

13: 19.15 Advantages of Symmetry

… ►Elliptic integrals are special cases of a particular multivariate hypergeometric function called Lauricella’s $F_D$ (Carlson (1961b)). …

14: 31.5 Solutions Analytic at Three Singularities: Heun Polynomials

… ►Some properties are included as special cases of properties given in §31.15 below.

15: 36.6 Scaling Relations

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Table 36.6.1: Special cases of scaling exponents for cuspoids.

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singularity	$K$	${\beta }_K$	${\gamma }_{1K}$	${\gamma }_{2K}$	${\gamma }_{3K}$	${\gamma }_K$
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16: 15.19 Methods of Computation

… ►This is because the linear transformations map the pair $\{{\mathrm{e}}^{\pi \mathrm{i}/3},{\mathrm{e}}^{-\pi \mathrm{i}/3}\}$ onto itself. …

17: 17.8 Special Cases of ${}_r{}^{}\psi _r^{}$ Functions

§17.8 Special Cases of ${}_r{}^{}\psi _r^{}$ Functions

… ►For similar formulas see Verma and Jain (1983).

18: 15.4 Special Cases

§15.4 Special Cases

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§15.4(i) Elementary Functions

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§15.4(ii) Argument Unity

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§15.4(iii) Other Arguments

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19: 18.8 Differential Equations

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20: 18.32 OP’s with Respect to Freud Weights

… ►Of special interest are the cases $Q(x)=x^{2m}$, $m=1,2,\mathrm{\dots }$, and the case $Q(x)=\frac{1}{4}{x}^4-t{x}^2$ ($t\in ℝ$), see §32.15. … ►The special case $Q(x)=\frac{1}{4}{x}^4-t{x}^2$ is of particular interest, see Clarkson and Jordaan (2018). …