DLMF:10.56.E4 (Q3768): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: hyperbolic sine function / rank
 
Normal rank
Property / Symbols used: hyperbolic sine function / qualifier
 
test:

sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}

\sinh@@{\NVar{z}}
Property / Symbols used: hyperbolic sine function / qualifier
 
xml-id: C4.S28.E1.m2adec
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: modified spherical Bessel function / rank
 
Normal rank
Property / Symbols used: modified spherical Bessel function / qualifier
 
test:

𝗂 n ( 2 ) ⁡ ( z ) spherical-Bessel-I-2 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)}}

\modsphBesseli{2}{\NVar{n}}@{\NVar{z}}
Property / Symbols used: modified spherical Bessel function / qualifier
 
xml-id: C10.S47.E8.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.m1cdec
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.m1cdec

Latest revision as of 14:16, 2 January 2020

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DLMF:10.56.E4
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    Statements

    test
    sinh ⁡ z 2 + 2 ⁢ i ⁢ z ⁢ t z = sinh ⁡ z z + ∑ n = 1 ∞ ( i ⁢ t ) n n ! ⁢ 𝗂 n - 1 ( 2 ) ⁡ ( z ) , superscript 𝑧 2 2 𝑖 𝑧 𝑡 𝑧 𝑧 𝑧 superscript subscript 𝑛 1 superscript 𝑖 𝑡 𝑛 𝑛 spherical-Bessel-I-2 𝑛 1 𝑧 {\displaystyle{\displaystyle\frac{\sinh\sqrt{z^{2}+2izt}}{z}=\frac{\sinh z}{z}% +\sum_{n=1}^{\infty}\frac{(it)^{n}}{n!}{\mathsf{i}^{(2)}_{n-1}}\left(z\right),}}
    0 references
    DLMF id
    DLMF:10.56.E4
    0 references
    Symbols used
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    hyperbolic sine function
    test
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    modified spherical Bessel function
    test
    𝗂 n ( 2 ) ⁡ ( z ) spherical-Bessel-I-2 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E8.m2adec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1cdec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1cdec
    0 references
     
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