DLMF:12.14.E14 (Q4254): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: Bessel function of the first kind / qualifier
 
test:

J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselJ{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the first kind / qualifier
 
xml-id: C10.S2.E2.m2aadec
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.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: Q11543 / rank
 
Normal rank
Property / Symbols used: Q11543 / qualifier
 
test:

W ⁡ ( a , x ) parabolic-W 𝑎 𝑥 {\displaystyle{\displaystyle W\left(\NVar{a},\NVar{x}\right)}}

\paraW@{\NVar{a}}{\NVar{x}}
Property / Symbols used: Q11543 / qualifier
 
xml-id: C12.S14.SS1.p1.m1ajdec
Property / Symbols used
 
Property / Symbols used: Q11520 / rank
 
Normal rank
Property / Symbols used: Q11520 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11520 / qualifier
 
xml-id: C12.S1.XMD1.m1jdec

Latest revision as of 14:28, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:12.14.E14
No description defined

    Statements

    test
    d d x ⁡ W ⁡ ( 0 , ± x ) = - 2 - 9 4 ⁢ x ⁢ π ⁢ x ⁢ ( J 3 4 ⁡ ( 1 4 ⁢ x 2 ) ± J - 3 4 ⁡ ( 1 4 ⁢ x 2 ) ) . derivative 𝑥 parabolic-W 0 plus-or-minus 𝑥 superscript 2 9 4 𝑥 𝜋 𝑥 plus-or-minus Bessel-J 3 4 1 4 superscript 𝑥 2 Bessel-J 3 4 1 4 superscript 𝑥 2 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}W\left(0,\pm x\right% )=-2^{-\frac{9}{4}}x\sqrt{\pi x}\left(J_{\frac{3}{4}}\left(\tfrac{1}{4}x^{2}% \right)\pm J_{-\frac{3}{4}}\left(\tfrac{1}{4}x^{2}\right)\right).}}
    0 references
    DLMF id
    DLMF:12.14.E14
    0 references
    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.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
    Q11543
    test
    W ⁡ ( a , x ) parabolic-W 𝑎 𝑥 {\displaystyle{\displaystyle W\left(\NVar{a},\NVar{x}\right)}}
    xml-id
    C12.S14.SS1.p1.m1ajdec
    0 references
    Q11520
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C12.S1.XMD1.m1jdec
    0 references
     
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