DLMF:8.6.E4 (Q2518): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1cdec

Latest revision as of 13:42, 2 January 2020

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DLMF:8.6.E4
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    Statements

    Defining formula
    Γ ⁡ ( a , z ) = z a ⁢ e - z Γ ⁡ ( 1 - a ) ⁢ ∫ 0 ∞ t - a ⁢ e - t z + t ⁢ d t , incomplete-Gamma 𝑎 𝑧 superscript 𝑧 𝑎 superscript 𝑒 𝑧 Euler-Gamma 1 𝑎 superscript subscript 0 superscript 𝑡 𝑎 superscript 𝑒 𝑡 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=\frac{z^{a}e^{-z}}{\Gamma% \left(1-a\right)}\int_{0}^{\infty}\frac{t^{-a}e^{-t}}{z+t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:8.6.E4
    0 references
    constraint
    | ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}
    0 references
    ℜ ⁡ a < 1 𝑎 1 {\displaystyle{\displaystyle\Re a<1}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    incomplete gamma function
    Defining formula
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1cdec
    0 references
    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1cdec
    0 references
     
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