DLMF:25.4.E2 (Q7609): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aadec

Revision as of 12:23, 2 January 2020

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DLMF:25.4.E2
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    Statements

    test
    ζ ⁡ ( s ) = 2 ⁢ ( 2 ⁢ π ) s - 1 ⁢ sin ⁡ ( 1 2 ⁢ π ⁢ s ) ⁢ Γ ⁡ ( 1 - s ) ⁢ ζ ⁡ ( 1 - s ) . Riemann-zeta 𝑠 2 superscript 2 𝜋 𝑠 1 1 2 𝜋 𝑠 Euler-Gamma 1 𝑠 Riemann-zeta 1 𝑠 {\displaystyle{\displaystyle\zeta\left(s\right)=2(2\pi)^{s-1}\sin\left(\tfrac{% 1}{2}\pi s\right)\Gamma\left(1-s\right)\zeta\left(1-s\right).}}
    0 references
    DLMF id
    DLMF:25.4.E2
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Riemann zeta function
    test
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
     
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