DLMF:12.14.E13 (Q4253): Difference between revisions

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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.m1aidec

Revision as of 14:28, 2 January 2020

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DLMF:12.14.E13
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    Statements

    test
    W ⁡ ( 0 , ± x ) = 2 - 5 4 ⁢ π ⁢ x ⁢ ( J - 1 4 ⁡ ( 1 4 ⁢ x 2 ) ∓ J 1 4 ⁡ ( 1 4 ⁢ x 2 ) ) , parabolic-W 0 plus-or-minus 𝑥 superscript 2 5 4 𝜋 𝑥 minus-or-plus Bessel-J 1 4 1 4 superscript 𝑥 2 Bessel-J 1 4 1 4 superscript 𝑥 2 {\displaystyle{\displaystyle W\left(0,\pm x\right)=2^{-\frac{5}{4}}\sqrt{\pi x% }\left(J_{-\frac{1}{4}}\left(\tfrac{1}{4}x^{2}\right)\mp J_{\frac{1}{4}}\left(% \tfrac{1}{4}x^{2}\right)\right),}}
    0 references
    DLMF id
    DLMF:12.14.E13
    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.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    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.m1aidec
    0 references
     
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