DLMF:10.57.E1 (Q3770): Difference between revisions

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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.m2adec
Property / Symbols used
 
Property / Symbols used: spherical Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: spherical Bessel function of the first kind / qualifier
 
test:

𝗃 n ⁡ ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}

\sphBesselJ{\NVar{n}}@{\NVar{z}}
Property / Symbols used: spherical Bessel function of the first kind / qualifier
 
xml-id: C10.S47.E3.m2adec
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.m1dec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1dec

Latest revision as of 13:17, 2 January 2020

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DLMF:10.57.E1
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    Statements

    test
    𝗃 n ′ ⁡ ( ( n + 1 2 ) ⁢ z ) = π 1 2 ( ( 2 ⁢ n + 1 ) ⁢ z ) 1 2 ⁢ J n + 1 2 ′ ⁡ ( ( n + 1 2 ) ⁢ z ) - π 1 2 ( ( 2 ⁢ n + 1 ) ⁢ z ) 3 2 ⁢ J n + 1 2 ⁡ ( ( n + 1 2 ) ⁢ z ) . diffop spherical-Bessel-J 𝑛 1 𝑛 1 2 𝑧 superscript 𝜋 1 2 superscript 2 𝑛 1 𝑧 1 2 diffop Bessel-J 𝑛 1 2 1 𝑛 1 2 𝑧 superscript 𝜋 1 2 superscript 2 𝑛 1 𝑧 3 2 Bessel-J 𝑛 1 2 𝑛 1 2 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{n}'\left((n+\tfrac{1}{2})z\right)=% \frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{1}{2}}}J_{n+\frac{1}{2}}'\left((n+% \tfrac{1}{2})z\right)-\frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{3}{2}}}J_{n+% \frac{1}{2}}\left((n+\tfrac{1}{2})z\right).}}
    0 references
    DLMF id
    DLMF:10.57.E1
    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.m2adec
    0 references
    spherical Bessel function of the first kind
    test
    𝗃 n ⁡ ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E3.m2adec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1dec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1dec
    0 references
     
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