error and related functions

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1: 14 Legendre and Related Functions

Chapter 14 Legendre and Related Functions

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2: 11 Struve and Related Functions

Chapter 11 Struve and Related Functions

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3: 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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4: 13.18 Relations to Other Functions

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§13.18(ii) Incomplete Gamma Functions

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5: 13.6 Relations to Other Functions

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§13.6(ii) Incomplete Gamma Functions

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6: 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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7: 7.18 Repeated Integrals of the Complementary Error Function

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7.18.6 $${\mathrm{i}}^n\mathrm{erfc}\left(z\right)=\sum _{k=0}^{\mathrm{\infty }}\frac{{(-1)}^k{z}^k}{2^{n-k}k!\mathrm{\Gamma }\left(1+\frac{1}{2}(n-k)\right)}.$$

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Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, $!$: factorial (as in $n!$), ${\mathrm{i}}^n\mathrm{erfc}\left(z\right)$: repeated integrals of the complementary error function, $z$: complex variable and $n$: nonnegative integer

A&S Ref:

7.2.4

Permalink:

http://dlmf.nist.gov/7.18.E6

Encodings:

pMML, png, TeX

See also:

Annotations for §7.18(iii), §7.18 and Ch.7

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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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8: 7.1 Special Notation

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9: 14.3 Definitions and Hypergeometric Representations

§14.3 Definitions and Hypergeometric Representations

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§14.3(i) Interval

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§14.3(ii) Interval

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§14.3(iii) Alternative Hypergeometric Representations

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§14.3(iv) Relations to Other Functions

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10: 7.5 Interrelations

§7.5 Interrelations

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