DLMF:2.6.E44 (Q870): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2afdec

Revision as of 16:16, 1 January 2020

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DLMF:2.6.E44
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    t μ - 1 f = s = 0 n - 1 ( - 1 ) s a s μ s ! D s + 1 ( t μ ( ln t - γ - ψ ( μ + 1 ) ) ) - s = 1 n d 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 superscript 1 𝑠 subscript 𝑎 𝑠 𝜇 𝑠 superscript 𝐷 𝑠 1 superscript 𝑡 𝜇 𝑡 digamma 𝜇 1 superscript subscript 𝑠 1 𝑛 subscript 𝑑 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}\frac{(-1)^{s}a_{% s}}{\mu\cdot s!}D^{s+1}\left(t^{\mu}\left(\ln t-\gamma-\psi\left(\mu+1\right)% \right)\right)-\sum_{s=1}^{n}d_{s}\frac{\Gamma\left(\mu\right)}{\Gamma\left(% \mu-s+1\right)}t^{\mu-s}+t^{\mu-1}\ast f_{n}}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2afdec
    0 references