DLMF:13.9.E12 (Q4455): Difference between revisions

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Property / constraint
 

Γ ( a ) Γ ( a - b + 1 ) < 0 Euler-Gamma 𝑎 Euler-Gamma 𝑎 𝑏 1 0 {\displaystyle{\displaystyle\Gamma\left(a\right)\Gamma\left(a-b+1\right)<0}}

\EulerGamma@{a}\EulerGamma@{a-b+1}<0
Property / constraint: Γ ( a ) Γ ( a - b + 1 ) < 0 Euler-Gamma 𝑎 Euler-Gamma 𝑎 𝑏 1 0 {\displaystyle{\displaystyle\Gamma\left(a\right)\Gamma\left(a-b+1\right)<0}} / rank
 
Normal rank
Property / constraint
 

a < 0 𝑎 0 {\displaystyle{\displaystyle a<0}}

a<0
Property / constraint: a < 0 𝑎 0 {\displaystyle{\displaystyle a<0}} / rank
 
Normal rank
Property / constraint
 

Γ ( a ) Γ ( a - b + 1 ) < 0 Γ 𝑎 Γ 𝑎 𝑏 1 0 {\displaystyle{\displaystyle\Gamma\left(a\right)\Gamma\left(a-b+1\right)<0}}

\Gamma\left(a\right)\Gamma\left(a-b+1\right)<0
Property / constraint: Γ ( a ) Γ ( a - b + 1 ) < 0 Γ 𝑎 Γ 𝑎 𝑏 1 0 {\displaystyle{\displaystyle\Gamma\left(a\right)\Gamma\left(a-b+1\right)<0}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11169 / rank
 
Normal rank
Property / Symbols used: Q11169 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}

\floor{\NVar{x}}
Property / Symbols used: Q11169 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r17.m4acdec
Property / Symbols used
 
Property / Symbols used: Q11578 / rank
 
Normal rank
Property / Symbols used: Q11578 / qualifier
 
Defining formula:

T ( a , b ) 𝑇 𝑎 𝑏 {\displaystyle{\displaystyle T(a,b)}}

T(a,b)
Property / Symbols used: Q11578 / qualifier
 
xml-id: C13.S9.XMD7.m1adec

Latest revision as of 16:00, 2 January 2020

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DLMF:13.9.E12
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    Statements

    T ( a , b ) = - a , 𝑇 𝑎 𝑏 𝑎 {\displaystyle{\displaystyle T(a,b)=\left\lfloor-a\right\rfloor,}}
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    DLMF:13.9.E12
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    Γ ( a ) Γ ( a - b + 1 ) < 0 Euler-Gamma 𝑎 Euler-Gamma 𝑎 𝑏 1 0 {\displaystyle{\displaystyle\Gamma\left(a\right)\Gamma\left(a-b+1\right)<0}}
    0 references
    a < 0 𝑎 0 {\displaystyle{\displaystyle a<0}}
    0 references
    Γ ( a ) Γ ( a - b + 1 ) < 0 Γ 𝑎 Γ 𝑎 𝑏 1 0 {\displaystyle{\displaystyle\Gamma\left(a\right)\Gamma\left(a-b+1\right)<0}}
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2abdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    introduction.Sx4.p1.t1.r17.m4acdec
    0 references
    T ( a , b ) 𝑇 𝑎 𝑏 {\displaystyle{\displaystyle T(a,b)}}
    C13.S9.XMD7.m1adec
    0 references