DLMF:10.22.E42 (Q3416): Difference between revisions

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Property / constraint
 

| ν | < 1 𝜈 1 {\displaystyle{\displaystyle|\Re\nu|<1}}

|\realpart@@{\nu}|<1
Property / constraint: | ν | < 1 𝜈 1 {\displaystyle{\displaystyle|\Re\nu|<1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Bessel function of the second kind / rank
 
Normal rank
Property / Symbols used: Bessel function of the second kind / qualifier
 
test:

Y ν ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselY{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the second kind / qualifier
 
xml-id: C10.S2.E3.m2addec
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.m2apdec
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.m1aaodec
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.m3aaodec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1awdec
Property / Symbols used
 
Property / Symbols used: tangent function / rank
 
Normal rank
Property / Symbols used: tangent function / qualifier
 
test:

tan z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}

\tan@@{\NVar{z}}
Property / Symbols used: tangent function / qualifier
 
xml-id: C4.S14.E4.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1abdec

Latest revision as of 13:20, 2 January 2020

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DLMF:10.22.E42
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    Statements

    0 Y ν ( t ) d t = - tan ( 1 2 ν π ) , superscript subscript 0 Bessel-Y-Weber 𝜈 𝑡 𝑡 1 2 𝜈 𝜋 {\displaystyle{\displaystyle\int_{0}^{\infty}Y_{\nu}\left(t\right)\mathrm{d}t=% -\tan\left(\tfrac{1}{2}\nu\pi\right),}}
    0 references
    0 references
    | ν | < 1 𝜈 1 {\displaystyle{\displaystyle|\Re\nu|<1}}
    0 references
    Y ν ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E3.m2addec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2apdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aaodec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aaodec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1awdec
    0 references
    tan z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    C4.S14.E4.m2aadec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C10.S1.XMD7.m1abdec
    0 references