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

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11028 / rank
 
Normal rank
Property / Symbols used: Q11028 / qualifier
 
Defining formula:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11028 / qualifier
 
xml-id: C2.S6.XMD14.m1fdec

Revision as of 17:16, 1 January 2020

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DLMF:2.6.E43
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    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
     
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