Mellin–Barnes type

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1: 11.5 Integral Representations

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Mellin–Barnes Integrals

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2: 10.32 Integral Representations

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Mellin–Barnes Type

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Mellin–Barnes Type

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3: 15.6 Integral Representations

§15.6 Integral Representations

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Figure 15.6.1: $t$-plane. … Magnify

4: 12.5 Integral Representations

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§12.5(iii) Mellin–Barnes Integrals

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5: 8.6 Integral Representations

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Mellin–Barnes Integrals

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6: 8.19 Generalized Exponential Integral

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8.19.4 $$E_p\left(z\right)=\frac{z^{p-1}{\mathrm{e}}^{-z}}{\mathrm{\Gamma }\left(p\right)}{\int }_0^{\mathrm{\infty }}\frac{t^{p-1}{\mathrm{e}}^{-zt}}{1+t}dt,$$ , $\mathrm{\Re }p>0$.

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Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, $\pi$: the ratio of the circumference of a circle to its diameter, $dx$: differential of $x$ , $\mathrm{e}$: base of natural logarithm, $E_p\left(z\right)$: generalized exponential integral, $\int$: integral, $\mathrm{ph}$: phase, $\mathrm{\Re }$: real part, $z$: complex variable and $p$: parameter

Keywords:

Laplace transform, Mellin transform

Permalink:

http://dlmf.nist.gov/8.19.E4

Encodings:

pMML, png, TeX

See also:

Annotations for §8.19(i), §8.19(i), §8.19 and Ch.8

►Integral representations of Mellin–Barnes type for $E_p\left(z\right)$ follow immediately from (8.6.11), (8.6.12), and (8.19.1). …

7: 13.16 Integral Representations

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§13.16(iii) Mellin–Barnes Integrals

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8: 10.9 Integral Representations

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Mellin–Barnes Type Integrals

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Mellin–Barnes Type

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9: 13.4 Integral Representations

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§13.4(iii) Mellin–Barnes Integrals

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10: 9.12 Scorer Functions

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Mellin–Barnes Type Integral

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