relation to error functions

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1: 7.11 Relations to Other Functions

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Incomplete Gamma Functions and Generalized Exponential Integral

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Confluent Hypergeometric Functions

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2: 7.1 Special Notation

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3: 7.5 Interrelations

§7.5 Interrelations

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4: 12.7 Relations to Other Functions

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§12.7(ii) Error Functions, Dawson’s Integral, and Probability Function

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5: 7.18 Repeated Integrals of the Complementary Error Function

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Hermite Polynomials

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Confluent Hypergeometric Functions

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Parabolic Cylinder Functions

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Probability Functions

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6: 13.18 Relations to Other Functions

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§13.18(ii) Incomplete Gamma Functions

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7: 7.19 Voigt Functions

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7.19.2 $$𝖵(x,t)=\frac{1}{\sqrt{4\pi t}}{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{y{\mathrm{e}}^{-{(x-y)}^2/(4t)}}{1+y^2}dy.$$

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Defines:

$𝖵(x,t)$: Voigt function

Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $dx$: differential of $x$ , $\mathrm{e}$: base of natural logarithm, $\int$: integral and $x$: real variable

Referenced by:

§7.19(iii)

Permalink:

http://dlmf.nist.gov/7.19.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §7.19(i), §7.19 and Ch.7

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8: 13.6 Relations to Other Functions

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§13.6(ii) Incomplete Gamma Functions

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9: 7.10 Derivatives

§7.10 Derivatives

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10: 7.13 Zeros

… ►In consequence of (7.5.5) and (7.5.10), zeros of $ℱ\left(z\right)$ are related to zeros of $\mathrm{erfc}z$. …