DLMF:2.6.E52 (Q878): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: fractional integral (locally) / rank
 
Normal rank
Property / Symbols used: fractional integral (locally) / qualifier
 
test:

I μ superscript 𝐼 𝜇 {\displaystyle{\displaystyle I^{\mu}}}

I^{\mu}
Property / Symbols used: fractional integral (locally) / qualifier
 
xml-id: C2.S6.XMD15.m1fdec
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.m1aadec
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.m1jdec
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.m1cdec

Latest revision as of 16:18, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:2.6.E52
No description defined

    Statements

    test
    I μ ⁢ f ⁢ ( x ) = ∑ s = 0 n - 1 ( - 1 ) s ⁢ Γ ⁡ ( 1 - s - α ) Γ ⁡ ( μ + 1 - s - α ) ⁢ x μ - s - α - π sin ⁡ ( π ⁢ α ) ⁢ ∑ s = 1 n 1 Γ ⁡ ( μ + 1 - s ) ⁢ x μ - s ( s - 1 ) ! + 1 x n ⁢ δ n ⁢ ( x ) . superscript 𝐼 𝜇 𝑓 𝑥 superscript subscript 𝑠 0 𝑛 1 superscript 1 𝑠 Euler-Gamma 1 𝑠 𝛼 Euler-Gamma 𝜇 1 𝑠 𝛼 superscript 𝑥 𝜇 𝑠 𝛼 𝜋 𝜋 𝛼 superscript subscript 𝑠 1 𝑛 1 Euler-Gamma 𝜇 1 𝑠 superscript 𝑥 𝜇 𝑠 𝑠 1 1 superscript 𝑥 𝑛 subscript 𝛿 𝑛 𝑥 {\displaystyle{\displaystyle I^{\mu}f(x)=\sum_{s=0}^{n-1}(-1)^{s}\frac{\Gamma% \left(1-s-\alpha\right)}{\Gamma\left(\mu+1-s-\alpha\right)}x^{\mu-s-\alpha}-% \frac{\pi}{\sin\left(\pi\alpha\right)}\sum_{s=1}^{n}\frac{1}{\Gamma\left(\mu+1% -s\right)}\frac{x^{\mu-s}}{(s-1)!}+\frac{1}{x^{n}}\delta_{n}(x).}}
    0 references
    DLMF id
    DLMF:2.6.E52
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2akdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5ajdec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2acdec
    0 references
    Q11028
    test
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C2.S6.XMD14.m1ldec
    0 references
    fractional integral (locally)
    test
    I μ superscript 𝐼 𝜇 {\displaystyle{\displaystyle I^{\mu}}}
    xml-id
    C2.S6.XMD15.m1fdec
    0 references
    Q11019
    test
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C2.S6.XMD2.m1aadec
    0 references
    Q11031
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S6.XMD20.m1jdec
    0 references
    Q11036
    test
    δ n ⁢ ( x ) subscript 𝛿 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}(x)}}
    xml-id
    C2.S6.XMD25.m1cdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q878&oldid=4932"