DLMF:10.43.E15 (Q3629): Difference between revisions

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

Ki α ⁡ ( x ) Bickley-Ki 𝛼 𝑥 {\displaystyle{\displaystyle\mathrm{Ki}_{\NVar{\alpha}}\left(\NVar{x}\right)}}

\BickleyKi{\NVar{\alpha}}@{\NVar{x}}
Property / Symbols used: Bickley function / qualifier
 
xml-id: C10.S43.E11.m2addec
Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
test:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2adec
Property / Symbols used
 
Property / Symbols used: modified Bessel function of the second kind / rank
 
Normal rank
Property / Symbols used: modified Bessel function of the second kind / qualifier
 
test:

K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modBesselK{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Bessel function of the second kind / qualifier
 
xml-id: C10.S25.E3.m2aedec
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.m1adec
Property / Symbols used
 
Property / Symbols used: Q11435 / rank
 
Normal rank
Property / Symbols used: Q11435 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11435 / qualifier
 
xml-id: C10.S1.XMD4.m1kdec

Latest revision as of 13:01, 2 January 2020

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DLMF:10.43.E15
No description defined

    Statements

    test
    Ki - n ⁡ ( x ) = ( - 1 ) n ⁢ d n d x n ⁡ K 0 ⁡ ( x ) , Bickley-Ki 𝑛 𝑥 superscript 1 𝑛 derivative 𝑥 𝑛 modified-Bessel-second-kind 0 𝑥 {\displaystyle{\displaystyle\mathrm{Ki}_{-n}\left(x\right)=(-1)^{n}\frac{{% \mathrm{d}}^{n}}{{\mathrm{d}x}^{n}}K_{0}\left(x\right),}}
    0 references
    DLMF id
    DLMF:10.43.E15
    0 references
    constraint
    n = 1 , 2 , 3 , … 𝑛 1 2 3 … {\displaystyle{\displaystyle n=1,2,3,\ldots}}
    0 references
    Symbols used
    Bickley function
    test
    Ki α ⁡ ( x ) Bickley-Ki 𝛼 𝑥 {\displaystyle{\displaystyle\mathrm{Ki}_{\NVar{\alpha}}\left(\NVar{x}\right)}}
    xml-id
    C10.S43.E11.m2addec
    0 references
    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2adec
    0 references
    modified Bessel function of the second kind
    test
    K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E3.m2aedec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1adec
    0 references
    Q11435
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1kdec
    0 references
     
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