DLMF:2.6.E45 (Q871): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11019 / rank
 
Normal rank
Property / Symbols used: Q11019 / qualifier
 
test:

f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}

f(t)
Property / Symbols used: Q11019 / qualifier
 
xml-id: C2.S6.XMD2.m1vdec
Property / Symbols used
 
Property / Symbols used: Q11031 / rank
 
Normal rank
Property / Symbols used: Q11031 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11031 / qualifier
 
xml-id: C2.S6.XMD20.m1edec
Property / Symbols used
 
Property / Symbols used: Q11034 / rank
 
Normal rank
Property / Symbols used: Q11034 / qualifier
 
test:

a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}

a_{n}
Property / Symbols used: Q11034 / qualifier
 
xml-id: C2.S6.XMD24.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11036 / rank
 
Normal rank
Property / Symbols used: Q11036 / qualifier
 
test:

δ n ⁢ ( x ) subscript 𝛿 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}(x)}}

\delta_{n}(x)
Property / Symbols used: Q11036 / qualifier
 
xml-id: C2.S6.XMD25.m1dec
Property / Symbols used
 
Property / Symbols used: Q11035 / rank
 
Normal rank
Property / Symbols used: Q11035 / qualifier
 
test:

c s subscript 𝑐 𝑠 {\displaystyle{\displaystyle c_{s}}}

c_{s}
Property / Symbols used: Q11035 / qualifier
 
xml-id: C2.S6.XMD9.m1bdec

Latest revision as of 16:17, 1 January 2020

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English
DLMF:2.6.E45
No description defined

    Statements

    test
    I μ ⁢ f ⁢ ( x ) = ∑ s = 0 n - 1 a s ⁢ Γ ⁡ ( 1 - s - α ) Γ ⁡ ( μ + 1 - s - α ) ⁢ x μ - s - α - ∑ s = 1 n c s Γ ⁡ ( μ + 1 - s ) ⁢ x μ - s + 1 x n ⁢ δ n ⁢ ( x ) , superscript 𝐼 𝜇 𝑓 𝑥 superscript subscript 𝑠 0 𝑛 1 subscript 𝑎 𝑠 Euler-Gamma 1 𝑠 𝛼 Euler-Gamma 𝜇 1 𝑠 𝛼 superscript 𝑥 𝜇 𝑠 𝛼 superscript subscript 𝑠 1 𝑛 subscript 𝑐 𝑠 Euler-Gamma 𝜇 1 𝑠 superscript 𝑥 𝜇 𝑠 1 superscript 𝑥 𝑛 subscript 𝛿 𝑛 𝑥 {\displaystyle{\displaystyle I^{\mu}f(x)=\sum_{s=0}^{n-1}a_{s}\frac{\Gamma% \left(1-s-\alpha\right)}{\Gamma\left(\mu+1-s-\alpha\right)}x^{\mu-s-\alpha}-% \sum_{s=1}^{n}\frac{c_{s}}{\Gamma\left(\mu+1-s\right)}x^{\mu-s}+\frac{1}{x^{n}% }\delta_{n}(x),}}
    0 references
    DLMF id
    DLMF:2.6.E45
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2agdec
    0 references
    Q11028
    test
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C2.S6.XMD14.m1hdec
    0 references
    fractional integral (locally)
    test
    I μ superscript 𝐼 𝜇 {\displaystyle{\displaystyle I^{\mu}}}
    xml-id
    C2.S6.XMD15.m1bdec
    0 references
    Q11019
    test
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C2.S6.XMD2.m1vdec
    0 references
    Q11031
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S6.XMD20.m1edec
    0 references
    Q11034
    test
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C2.S6.XMD24.m1ddec
    0 references
    Q11036
    test
    δ n ⁢ ( x ) subscript 𝛿 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}(x)}}
    xml-id
    C2.S6.XMD25.m1dec
    0 references
    Q11035
    test
    c s subscript 𝑐 𝑠 {\displaystyle{\displaystyle c_{s}}}
    xml-id
    C2.S6.XMD9.m1bdec
    0 references
     
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