DLMF:9.7.E3 (Q2810): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10769 / rank
 
Normal rank
Property / Symbols used: Q10769 / qualifier
 
Defining formula:

≡ equal-by definition {\displaystyle{\displaystyle\equiv}}

\defeq
Property / Symbols used: Q10769 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r9.m2adec

Latest revision as of 14:31, 2 January 2020

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DLMF:9.7.E3
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    Statements

    Defining formula
    χ ⁢ ( x ) ≡ π 1 / 2 ⁢ Γ ⁡ ( 1 2 ⁢ x + 1 ) / Γ ⁡ ( 1 2 ⁢ x + 1 2 ) . equal-by definition 𝜒 𝑥 1 2 Euler-Gamma 1 2 𝑥 1 Euler-Gamma 1 2 𝑥 1 2 {\displaystyle{\displaystyle\chi(x)\equiv{\pi^{\ifrac{1}{2}}}\Gamma\left(% \tfrac{1}{2}x+1\right)/\Gamma\left(\tfrac{1}{2}x+\tfrac{1}{2}\right).}}
    0 references
    DLMF id
    DLMF:9.7.E3
    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.m2adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q10769
    Defining formula
    ≡ equal-by definition {\displaystyle{\displaystyle\equiv}}
    xml-id
    introduction.Sx4.p1.t1.r9.m2adec
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