DLMF:10.43.E21 (Q3635): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10901 / rank
 
Normal rank
Property / Symbols used: Q10901 / qualifier
 
test:

absent {\displaystyle{\displaystyle\Im}}

\imagpart@@
Property / Symbols used: Q10901 / qualifier
 
xml-id: C1.S9.E2.m2aadec
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.m3apdec
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.m2aidec
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.m2adec

Latest revision as of 14:02, 2 January 2020

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DLMF:10.43.E21
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    Statements

    0 sin ( a t ) K 0 ( t ) d t = arcsinh a ( 1 + a 2 ) 1 2 , superscript subscript 0 𝑎 𝑡 modified-Bessel-second-kind 0 𝑡 𝑡 hyperbolic-inverse-sine 𝑎 superscript 1 superscript 𝑎 2 1 2 {\displaystyle{\displaystyle\int_{0}^{\infty}\sin\left(at\right)K_{0}\left(t% \right)\mathrm{d}t=\frac{\operatorname{arcsinh}a}{(1+a^{2})^{\frac{1}{2}}},}}
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    | a | < 1 𝑎 1 {\displaystyle{\displaystyle|\Im a|<1}}
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1apdec
    0 references
    arcsinh z hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}
    C4.S37.SS2.p1.m8adec
    0 references
    absent {\displaystyle{\displaystyle\Im}}
    C1.S9.E2.m2aadec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3apdec
    0 references
    K ν ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S25.E3.m2aidec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2adec
    0 references