DLMF:32.11.E18 (Q9453): Difference between revisions

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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: 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
 
Defining formula:

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.m2addec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
Defining formula:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1abdec
Property / Symbols used
 
Property / Symbols used: Q12571 / rank
 
Normal rank
Property / Symbols used: Q12571 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12571 / qualifier
 
xml-id: C32.S1.XMD2.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12638 / rank
 
Normal rank
Property / Symbols used: Q12638 / qualifier
 
Defining formula:

χ 𝜒 {\displaystyle{\displaystyle\chi}}

\chi
Property / Symbols used: Q12638 / qualifier
 
xml-id: C32.S11.XMD10.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12640 / rank
 
Normal rank
Property / Symbols used: Q12640 / qualifier
 
Defining formula:

d 𝑑 {\displaystyle{\displaystyle d}}

d
Property / Symbols used: Q12640 / qualifier
 
xml-id: C32.S11.XMD9.m1ddec

Latest revision as of 14:15, 2 January 2020

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DLMF:32.11.E18
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    Statements

    χ + 3 2 d 2 ln 2 - 1 4 π - ph Γ ( 1 2 i d 2 ) n π , 𝜒 3 2 superscript 𝑑 2 2 1 4 𝜋 phase Euler-Gamma 1 2 𝑖 superscript 𝑑 2 𝑛 𝜋 {\displaystyle{\displaystyle\chi+\tfrac{3}{2}d^{2}\ln 2-\tfrac{1}{4}\pi-% \operatorname{ph}\Gamma\left(\tfrac{1}{2}id^{2}\right)\neq n\pi,}}
    0 references
    DLMF:32.11.E18
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2abdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2addec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2abdec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2ahdec
    0 references
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1abdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C32.S1.XMD2.m1bdec
    0 references
    χ 𝜒 {\displaystyle{\displaystyle\chi}}
    C32.S11.XMD10.m1bdec
    0 references
    d 𝑑 {\displaystyle{\displaystyle d}}
    C32.S11.XMD9.m1ddec
    0 references