DLMF:18.35.E6 (Q6045): Difference between revisions

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Property / constraint
 

0 < θ < π 0 𝜃 𝜋 {\displaystyle{\displaystyle 0<\theta<\pi}}

0<\theta<\pi
Property / constraint: 0 < θ < π 0 𝜃 𝜋 {\displaystyle{\displaystyle 0<\theta<\pi}} / rank
 
Normal rank
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.m2adec
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
Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
test:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11729 / rank
 
Normal rank
Property / Symbols used: Q11729 / qualifier
 
test:

w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}

w(x)
Property / Symbols used: Q11729 / qualifier
 
xml-id: C18.S1.XMD10.m1adec
Property / Symbols used
 
Property / Symbols used: DLMF:18.35.E3 / rank
 
Normal rank
Property / Symbols used: DLMF:18.35.E3 / qualifier
 
test:

τ a , b ⁢ ( θ ) subscript 𝜏 𝑎 𝑏 𝜃 {\displaystyle{\displaystyle\tau_{a,b}(\theta)}}

\tau_{a,b}(\theta)
Property / Symbols used: DLMF:18.35.E3 / qualifier
 
xml-id: C18.S35.XMD1.m1bdec

Latest revision as of 12:30, 2 January 2020

No description defined
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English
DLMF:18.35.E6
No description defined

    Statements

    test
    w ( λ ) ⁢ ( cos ⁡ θ ; a , b ) = π - 1 ⁢ 2 2 ⁢ λ - 1 ⁢ e ( 2 ⁢ θ - π ) ⁢ τ a , b ⁢ ( θ ) ⁢ ( sin ⁡ θ ) 2 ⁢ λ - 1 ⁢ | Γ ⁡ ( λ + i ⁢ τ a , b ⁢ ( θ ) ) | 2 , superscript 𝑤 𝜆 𝜃 𝑎 𝑏 superscript 𝜋 1 superscript 2 2 𝜆 1 superscript 𝑒 2 𝜃 𝜋 subscript 𝜏 𝑎 𝑏 𝜃 superscript 𝜃 2 𝜆 1 Euler-Gamma 𝜆 imaginary-unit subscript 𝜏 𝑎 𝑏 𝜃 2 {\displaystyle{\displaystyle w^{(\lambda)}(\cos\theta;a,b)=\pi^{-1}\*2^{2% \lambda-1}\*e^{(2\theta-\pi)\*\tau_{a,b}(\theta)}\*(\sin\theta)^{2\lambda-1}\*% {\left|\Gamma\left(\lambda+\mathrm{i}\tau_{a,b}(\theta)\right)\right|^{2}},}}
    0 references
    DLMF id
    DLMF:18.35.E6
    0 references
    constraint
    0 < θ < π 0 𝜃 𝜋 {\displaystyle{\displaystyle 0<\theta<\pi}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    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
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    Q11729
    test
    w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    xml-id
    C18.S1.XMD10.m1adec
    0 references
    DLMF:18.35.E3
    test
    τ a , b ⁢ ( θ ) subscript 𝜏 𝑎 𝑏 𝜃 {\displaystyle{\displaystyle\tau_{a,b}(\theta)}}
    xml-id
    C18.S35.XMD1.m1bdec
    0 references
     
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