DLMF:8.7.E4 (Q2530): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2acdec
Property / Symbols used
 
Property / Symbols used: incomplete gamma function / rank
 
Normal rank
Property / Symbols used: incomplete gamma function / qualifier
 
test:

γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}

\incgamma@{\NVar{a}}{\NVar{z}}
Property / Symbols used: incomplete gamma function / qualifier
 
xml-id: C8.S2.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: modified Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: modified Bessel function of the first kind / qualifier
 
test:

I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modBesselI{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Bessel function of the first kind / qualifier
 
xml-id: C10.S25.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q11332 / rank
 
Normal rank
Property / Symbols used: Q11332 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11332 / qualifier
 
xml-id: C8.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11329 / rank
 
Normal rank
Property / Symbols used: Q11329 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11329 / qualifier
 
xml-id: C8.S1.XMD6.m1adec
Property / Symbols used
 
Property / Symbols used: functions (locally) / rank
 
Normal rank
Property / Symbols used: functions (locally) / qualifier
 
test:

e n ⁢ ( z ) subscript 𝑒 𝑛 𝑧 {\displaystyle{\displaystyle e_{n}(z)}}

e_{n}(z)
Property / Symbols used: functions (locally) / qualifier
 
xml-id: C8.S4.XMD1.m1adec

Latest revision as of 12:46, 2 January 2020

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DLMF:8.7.E4
No description defined

    Statements

    test
    γ ⁡ ( a , x ) = Γ ⁡ ( a ) ⁢ x 1 2 ⁢ a ⁢ e - x ⁢ ∑ n = 0 ∞ e n ⁢ ( - 1 ) ⁢ x 1 2 ⁢ n ⁢ I n + a ⁡ ( 2 ⁢ x 1 / 2 ) , incomplete-gamma 𝑎 𝑥 Euler-Gamma 𝑎 superscript 𝑥 1 2 𝑎 superscript 𝑒 𝑥 superscript subscript 𝑛 0 subscript 𝑒 𝑛 1 superscript 𝑥 1 2 𝑛 modified-Bessel-first-kind 𝑛 𝑎 2 superscript 𝑥 1 2 {\displaystyle{\displaystyle\gamma\left(a,x\right)=\Gamma\left(a\right)x^{% \frac{1}{2}a}e^{-x}\sum_{n=0}^{\infty}e_{n}(-1)x^{\frac{1}{2}n}I_{n+a}\left(% \textstyle 2x^{1/2}\right),}}
    0 references
    DLMF id
    DLMF:8.7.E4
    0 references
    constraint
    a ≠ 0 , - 1 , - 2 , … 𝑎 0 1 2 … {\displaystyle{\displaystyle a\neq 0,-1,-2,\dots}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    incomplete gamma function
    test
    γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E1.m2aadec
    0 references
    modified Bessel function of the first kind
    test
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2adec
    0 references
    Q11332
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1adec
    0 references
    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1cdec
    0 references
    Q11329
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C8.S1.XMD6.m1adec
    0 references
    functions (locally)
    test
    e n ⁢ ( z ) subscript 𝑒 𝑛 𝑧 {\displaystyle{\displaystyle e_{n}(z)}}
    xml-id
    C8.S4.XMD1.m1adec
    0 references
     
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