DLMF:2.6.E43 (Q869): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: convolution (locally) / rank
 
Normal rank
Property / Symbols used: convolution (locally) / qualifier
 
Defining formula:

∗ ∗ {\displaystyle{\displaystyle\ast}}

\ast
Property / Symbols used: convolution (locally) / qualifier
 
xml-id: C2.S6.XMD17.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11019 / rank
 
Normal rank
Property / Symbols used: Q11019 / qualifier
 
Defining formula:

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

f(t)
Property / Symbols used: Q11019 / qualifier
 
xml-id: C2.S6.XMD2.m1tdec
Property / Symbols used
 
Property / Symbols used: Q11031 / rank
 
Normal rank
Property / Symbols used: Q11031 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11031 / qualifier
 
xml-id: C2.S6.XMD20.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11034 / rank
 
Normal rank
Property / Symbols used: Q11034 / qualifier
 
Defining formula:

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

a_{n}
Property / Symbols used: Q11034 / qualifier
 
xml-id: C2.S6.XMD24.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11022 / rank
 
Normal rank
Property / Symbols used: Q11022 / qualifier
 
Defining formula:

f n , n ⁢ ( t ) subscript 𝑓 𝑛 𝑛 𝑡 {\displaystyle{\displaystyle f_{n,n}(t)}}

f_{n,n}(t)
Property / Symbols used: Q11022 / qualifier
 
xml-id: C2.S6.XMD7.m1idec
Property / Symbols used
 
Property / Symbols used: Q11035 / rank
 
Normal rank
Property / Symbols used: Q11035 / qualifier
 
Defining formula:

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

c_{s}
Property / Symbols used: Q11035 / qualifier
 
xml-id: C2.S6.XMD9.m1adec

Latest revision as of 17:16, 1 January 2020

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DLMF:2.6.E43
No description defined

    Statements

    Defining formula
    t μ - 1 ∗ f = ∑ s = 0 n - 1 a s ⁢ Γ ⁡ ( μ ) ⁢ Γ ⁡ ( 1 - s - α ) Γ ⁡ ( μ + 1 - s - α ) ⁢ t μ - s - α - ∑ s = 1 n c s ⁢ Γ ⁡ ( μ ) Γ ⁡ ( μ - s + 1 ) ⁢ t μ - s + t μ - 1 ∗ f n ∗ superscript 𝑡 𝜇 1 𝑓 superscript subscript 𝑠 0 𝑛 1 subscript 𝑎 𝑠 Euler-Gamma 𝜇 Euler-Gamma 1 𝑠 𝛼 Euler-Gamma 𝜇 1 𝑠 𝛼 superscript 𝑡 𝜇 𝑠 𝛼 superscript subscript 𝑠 1 𝑛 subscript 𝑐 𝑠 Euler-Gamma 𝜇 Euler-Gamma 𝜇 𝑠 1 superscript 𝑡 𝜇 𝑠 ∗ superscript 𝑡 𝜇 1 subscript 𝑓 𝑛 {\displaystyle{\displaystyle t^{\mu-1}\ast f=\sum_{s=0}^{n-1}a_{s}\frac{\Gamma% \left(\mu\right)\Gamma\left(1-s-\alpha\right)}{\Gamma\left(\mu+1-s-\alpha% \right)}t^{\mu-s-\alpha}-\sum_{s=1}^{n}c_{s}\frac{\Gamma\left(\mu\right)}{% \Gamma\left(\mu-s+1\right)}t^{\mu-s}+t^{\mu-1}\ast f_{n}}}
    0 references
    DLMF id
    DLMF:2.6.E43
    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.m2aedec
    0 references
    Q11028
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C2.S6.XMD14.m1fdec
    0 references
    convolution (locally)
    Defining formula
    ∗ ∗ {\displaystyle{\displaystyle\ast}}
    xml-id
    C2.S6.XMD17.m1gdec
    0 references
    Q11019
    Defining formula
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C2.S6.XMD2.m1tdec
    0 references
    Q11031
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S6.XMD20.m1cdec
    0 references
    Q11034
    Defining formula
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C2.S6.XMD24.m1bdec
    0 references
    Q11022
    Defining formula
    f n , n ⁢ ( t ) subscript 𝑓 𝑛 𝑛 𝑡 {\displaystyle{\displaystyle f_{n,n}(t)}}
    xml-id
    C2.S6.XMD7.m1idec
    0 references
    Q11035
    Defining formula
    c s subscript 𝑐 𝑠 {\displaystyle{\displaystyle c_{s}}}
    xml-id
    C2.S6.XMD9.m1adec
    0 references
     
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