DLMF:2.4.E3 (Q756): 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.m2adec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1abdec
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.m2abdec
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec
Property / Symbols used
 
Property / Symbols used: Q10973 / rank
 
Normal rank
Property / Symbols used: Q10973 / qualifier
 
test:

q ⁢ ( t ) 𝑞 𝑡 {\displaystyle{\displaystyle q(t)}}

q(t)
Property / Symbols used: Q10973 / qualifier
 
xml-id: C2.S4.XMD16.m1bdec
Property / Symbols used
 
Property / Symbols used: Q10975 / rank
 
Normal rank
Property / Symbols used: Q10975 / qualifier
 
test:

Q ⁢ ( z ) 𝑄 𝑧 {\displaystyle{\displaystyle Q(z)}}

Q(z)
Property / Symbols used: Q10975 / qualifier
 
xml-id: C2.S4.XMD6.m1adec
Property / Symbols used
 
Property / Symbols used: Q10976 / rank
 
Normal rank
Property / Symbols used: Q10976 / qualifier
 
test:

σ 𝜎 {\displaystyle{\displaystyle\sigma}}

\sigma
Property / Symbols used: Q10976 / qualifier
 
xml-id: C2.S4.XMD7.m1dec

Latest revision as of 15:56, 1 January 2020

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DLMF:2.4.E3
No description defined

    Statements

    test
    q ⁢ ( t ) = 1 2 ⁢ π ⁢ i ⁢ lim η → ∞ ⁡ ∫ σ - i ⁢ η σ + i ⁢ η e t ⁢ z ⁢ Q ⁢ ( z ) ⁢ d z , 𝑞 𝑡 1 2 𝜋 𝑖 subscript → 𝜂 superscript subscript 𝜎 𝑖 𝜂 𝜎 𝑖 𝜂 superscript 𝑒 𝑡 𝑧 𝑄 𝑧 𝑧 {\displaystyle{\displaystyle q(t)=\frac{1}{2\pi i}\lim\limits_{\eta\to\infty}% \int_{\sigma-i\eta}^{\sigma+i\eta}e^{tz}Q(z)\mathrm{d}z,}}
    0 references
    DLMF id
    DLMF:2.4.E3
    0 references
    constraint
    0 < t < ∞ 0 𝑡 {\displaystyle{\displaystyle 0<t<\infty}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q10973
    test
    q ⁢ ( t ) 𝑞 𝑡 {\displaystyle{\displaystyle q(t)}}
    xml-id
    C2.S4.XMD16.m1bdec
    0 references
    Q10975
    test
    Q ⁢ ( z ) 𝑄 𝑧 {\displaystyle{\displaystyle Q(z)}}
    xml-id
    C2.S4.XMD6.m1adec
    0 references
    Q10976
    test
    σ 𝜎 {\displaystyle{\displaystyle\sigma}}
    xml-id
    C2.S4.XMD7.m1dec
    0 references
     
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