DLMF:10.56.E5 (Q3769): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: exponential function / rank
 
Normal rank
Property / Symbols used: exponential function / qualifier
 
test:

exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}

\exp@@{\NVar{z}}
Property / Symbols used: exponential function / qualifier
 
xml-id: C4.S2.E19.m2adec
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5addec
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.m2abdec
Property / Symbols used
 
Property / Symbols used: modified spherical Bessel function / rank
 
Normal rank
Property / Symbols used: modified spherical Bessel function / qualifier
 
test:

𝗄 n ⁡ ( z ) spherical-Bessel-K 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{k}_{\NVar{n}}\left(\NVar{z}\right)}}

\modsphBesselK{\NVar{n}}@{\NVar{z}}
Property / Symbols used: modified spherical Bessel function / qualifier
 
xml-id: C10.S47.E9.m2adec
Property / Symbols used
 
Property / Symbols used: Q11429 / rank
 
Normal rank
Property / Symbols used: Q11429 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11429 / qualifier
 
xml-id: C10.S1.XMD2.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1ddec

Latest revision as of 13:17, 2 January 2020

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DLMF:10.56.E5
No description defined

    Statements

    test
    exp ⁡ ( - z 2 + 2 ⁢ i ⁢ z ⁢ t ) z = e - z z + 2 π ⁢ ∑ n = 1 ∞ ( - i ⁢ t ) n n ! ⁢ 𝗄 n - 1 ⁡ ( z ) . superscript 𝑧 2 2 𝑖 𝑧 𝑡 𝑧 superscript 𝑒 𝑧 𝑧 2 𝜋 superscript subscript 𝑛 1 superscript 𝑖 𝑡 𝑛 𝑛 spherical-Bessel-K 𝑛 1 𝑧 {\displaystyle{\displaystyle\frac{\exp\left(-\sqrt{z^{2}+2izt}\right)}{z}=% \frac{e^{-z}}{z}+\frac{2}{\pi}\sum_{n=1}^{\infty}\frac{(-it)^{n}}{n!}\mathsf{k% }_{n-1}\left(z\right).}}
    0 references
    DLMF id
    DLMF:10.56.E5
    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
    exponential function
    test
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5addec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    modified spherical Bessel function
    test
    𝗄 n ⁡ ( z ) spherical-Bessel-K 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{k}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E9.m2adec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1ddec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1ddec
    0 references
     
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